### Wednesday, February 27, 2008

## JSH: Bet it all, lose it all

One of my heroes is Sir Isaac Newton who it turns out was not exactly a nice guy. Later in life he had among other things the job of protecting the currency of Britain, so he could send criminals to be executed. He did his job.

Mathematics to me is about absolutes. So I can reach a point where I tend to think in absolutes, and after five years of facing a math society that clearly has lied repeatedly and has behaved as if it could not be caught, I've lost any interest in concerns about not acting from absolutes.

Modern mathematicians pushed the idea that proofs could be delicate things and talked of failed proofs. They claimed proofs were not discovered but were creations, and that whether an argument was a proof or not was about whether mathematicians thought it was a proof or not.

My take on the field is that it has been overtaken by fiction writers. People who see themselves as authors of "proofs" which are really entertainment for others like them as no one else can even comprehend this stuff.

So style is the most important thing for math undergrads to learn in this system.

Style.

I lost count of how many times people told me my mathematical arguments did not look like math proofs.

But I say proof is discovery, and so it can be like prospecting, hunting for gold treasure. Treasure seekers don't worry about the dressing, they worry about the goods. After all, they're rooting in dirt or streams. It's not a pretty process.

Fiction writers took over the math field and fiction writing is about conflict, and contradiction, or apparent contradiction can be part of conflict and good fiction, so math society believes in "logical contradiction" along with those "delicate proofs" that can be wrong.

But I am a discoverer. I search for mathematical proofs the way you go for gold or diamond hunting. And I don't appreciate a style society of fiction writers pretending to be mathematicians telling me my finds are not what I can prove they are.

You people of course have bet your careers on me not being able to convince anyone else, which I say is, fine. You want to bet, then fine, but you need to know that is what you are doing.

I am a no-nonsense person on these issues.

And I have no compunction with presiding over shutting down entire mathematical departments where I've said that I would definitely put the Princeton math department at the top of that list of departments that should just be shutdown.

If I am wrong, then you just have more ranting from someone many of you are quite willing to call a madman, but if I am right about my finds then you need to accept what will happen when I get past your fiction writing society, past all the blocks you've thrown up in what is increasingly clear is a conspiracy to commit fraud--and inform the world.

So they know you faked math discoveries for years and to prove you knew you were faking you blocked acceptance of my research for years and even kept up the game with the factoring problem which I turned to because I knew you couldn't successfully block a major research find in that area.

So you have bet it all.

Fine.

You people ultimately don't understand what mathematics is, or what mathematical proof is, or you would not have done it.

And that finally is my most potent argument explaining why there is no choice for the world—real mathematicians could not have failed to understand when it was over as a mathematical proof said it was over.

Therefore, you are not at all real mathematicians.

I have the theory. So it's not a question mathematically of whether or not it will work. It's just a matter of the implementation that the theory says must be there actually being presented, and then the entire sorry tale will be the talk of the entire world.

Mathematicians around the world fakes!!!—the headlines may read.

And you will have lost it all on your bets in what will turn out to be a much better story than any of you ever wrote in your fake "proofs", though its grandeur will be a lot about the heaviness of your fall.

Mathematics to me is about absolutes. So I can reach a point where I tend to think in absolutes, and after five years of facing a math society that clearly has lied repeatedly and has behaved as if it could not be caught, I've lost any interest in concerns about not acting from absolutes.

Modern mathematicians pushed the idea that proofs could be delicate things and talked of failed proofs. They claimed proofs were not discovered but were creations, and that whether an argument was a proof or not was about whether mathematicians thought it was a proof or not.

My take on the field is that it has been overtaken by fiction writers. People who see themselves as authors of "proofs" which are really entertainment for others like them as no one else can even comprehend this stuff.

So style is the most important thing for math undergrads to learn in this system.

Style.

I lost count of how many times people told me my mathematical arguments did not look like math proofs.

But I say proof is discovery, and so it can be like prospecting, hunting for gold treasure. Treasure seekers don't worry about the dressing, they worry about the goods. After all, they're rooting in dirt or streams. It's not a pretty process.

Fiction writers took over the math field and fiction writing is about conflict, and contradiction, or apparent contradiction can be part of conflict and good fiction, so math society believes in "logical contradiction" along with those "delicate proofs" that can be wrong.

But I am a discoverer. I search for mathematical proofs the way you go for gold or diamond hunting. And I don't appreciate a style society of fiction writers pretending to be mathematicians telling me my finds are not what I can prove they are.

You people of course have bet your careers on me not being able to convince anyone else, which I say is, fine. You want to bet, then fine, but you need to know that is what you are doing.

I am a no-nonsense person on these issues.

And I have no compunction with presiding over shutting down entire mathematical departments where I've said that I would definitely put the Princeton math department at the top of that list of departments that should just be shutdown.

If I am wrong, then you just have more ranting from someone many of you are quite willing to call a madman, but if I am right about my finds then you need to accept what will happen when I get past your fiction writing society, past all the blocks you've thrown up in what is increasingly clear is a conspiracy to commit fraud--and inform the world.

So they know you faked math discoveries for years and to prove you knew you were faking you blocked acceptance of my research for years and even kept up the game with the factoring problem which I turned to because I knew you couldn't successfully block a major research find in that area.

So you have bet it all.

Fine.

You people ultimately don't understand what mathematics is, or what mathematical proof is, or you would not have done it.

And that finally is my most potent argument explaining why there is no choice for the world—real mathematicians could not have failed to understand when it was over as a mathematical proof said it was over.

Therefore, you are not at all real mathematicians.

I have the theory. So it's not a question mathematically of whether or not it will work. It's just a matter of the implementation that the theory says must be there actually being presented, and then the entire sorry tale will be the talk of the entire world.

Mathematicians around the world fakes!!!—the headlines may read.

And you will have lost it all on your bets in what will turn out to be a much better story than any of you ever wrote in your fake "proofs", though its grandeur will be a lot about the heaviness of your fall.

## JSH: Stepping back

I've been pushing myself as hard as I can go to get to a practical implementation and I'm facing that I can't get it done tonight, but I'm hoping to be finished within the next couple of weeks with a working solution to the factoring problem fully programmed.

But I want to keep raising the stakes, but I think I shouldn't so I'm stepping back.

Problem solving is about finding what's necessary to get the solution and I think I have it now where getting to the answer was more than just figuring out the math, it was also about facing a steady stream of negativity, character assassination and questions about my sanity from people fighting their own battle to prevent the knowledge from being found.

And what knowledge.

The factoring problem can be attacked through what I call surrogate factoring by leveraging one factorization against another.

With

z^2 = y^2 + nT

where T is the target to be factored, z itself can be approximated, surprisingly enough by looking at a maximum value for a variable I call k, for which

abs(nT - (α^2+1)k^2)

is a minimum where '=E1' is yet another variable, which is chosen such that

k^2 = (α^2+1)^{-1}(nT) mod p

exists, where p is an odd prime of your choice.

It is preferred that z have 3 as a factor as in general it can be shown to have

(2=α^2+1)

as a factor, so for most values of 'α'—2 out of 3—it will at least have 3 as a factor, and who knew that factoring had all these relationships available?

But that's what can make mathematics exciting!!!

Interested readers can figure out the derivations on their own.

Key is letting 2αx = k + pr_2, and z = x + αk, and considering what happens if you move k about with k = k_0 + jp, and substituting into

z^2 = y^2 + nT

and then you can re-derive everything I have shown here. Easily.

x^2 = y^2 + nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2) - (k_0 + pj)pr_2

Seemingly complex it is the result of just doing the substitution and simplifying a bit with the given relations.

It shows that if you move k around with j, you will have a minimum absolute value for

nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2)

because x, y and nT are constant, as is α and k_0, so because the j^2 term will dominate r_2 will tend to be negative to compensate, and that allows you to get an idea of where k_0 is.

And if j=0, then z = (1+2α^2)k/(2α), so you have it explicitly.

The mathematics is what is commonly called elementary methods.

And I like simple.

I think about researchers around the world claiming to be working on the factoring problem who will say nothing about this research.

Weaklings.

Fakes.

That's me stepping back a bit. But I don't want these people staying in positions that they clearly are not filling later. So the warning to them is, yes, I want this research acknowledged before I fully force the situation, but when I do force it, if that is necessary, then the next problem I will solve will be making sure that none of them remain in the field as mathematicians or cryptographers, so they need to start thinking about what they will be doing for work, in the aftermath.

Or, show some goddamn sense, and just acknowledge the research now.

[A reply to someone who asked James whether or not he was thinking about doing some violent action.]

I'll admit that I'm still wary of the impact of a sudden change precipitated by me just factoring some really large number so I'd prefer buy-in from the cryptographic industry ahead of that event.

But make no mistake, if this impasse ends with me, say, factoring a large enough number to show this research must be viable, WITH the growing history now of an improper response from the cryptographic community then the likely impact will be a sharp loss of confidence in that industry.

But that industry would next be tasked with resolving the issue along with the high tech community so that secure transmissions could continue.

So the first major step would be just figuring out which of you are in on this cover-up or not, and even if you're not part of this particular cover-up, do you actually have real mathematical skills or are you a fake?

That could mean a snarl on looking for solutions, so yes, my putting out the theory now and talking about the research in-depth is methodical AND important.

Posters challenging me to just factor an RSA number are pushing the snarl, when if the research is viable the theory would show lots of indications that I could do so with plenty of time for proper industry action.

Given what I know about the current corruption in the mathematical community I'm not surprised by the behavior, but I'm still hopeful that there are some members of the cryptographic community who are legit.

Otherwise the snarl is what we will see down the line with the world—and I'm sure all major world leaders—facing the big issue of trying to figure out what to do when RSA encryption goes away, probably literally overnight, as it's potentially broken now by others, but we don't know that so it still works if only out of faith in it.

But I want to keep raising the stakes, but I think I shouldn't so I'm stepping back.

Problem solving is about finding what's necessary to get the solution and I think I have it now where getting to the answer was more than just figuring out the math, it was also about facing a steady stream of negativity, character assassination and questions about my sanity from people fighting their own battle to prevent the knowledge from being found.

And what knowledge.

The factoring problem can be attacked through what I call surrogate factoring by leveraging one factorization against another.

With

z^2 = y^2 + nT

where T is the target to be factored, z itself can be approximated, surprisingly enough by looking at a maximum value for a variable I call k, for which

abs(nT - (α^2+1)k^2)

is a minimum where '=E1' is yet another variable, which is chosen such that

k^2 = (α^2+1)^{-1}(nT) mod p

exists, where p is an odd prime of your choice.

It is preferred that z have 3 as a factor as in general it can be shown to have

(2=α^2+1)

as a factor, so for most values of 'α'—2 out of 3—it will at least have 3 as a factor, and who knew that factoring had all these relationships available?

But that's what can make mathematics exciting!!!

Interested readers can figure out the derivations on their own.

Key is letting 2αx = k + pr_2, and z = x + αk, and considering what happens if you move k about with k = k_0 + jp, and substituting into

z^2 = y^2 + nT

and then you can re-derive everything I have shown here. Easily.

x^2 = y^2 + nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2) - (k_0 + pj)pr_2

Seemingly complex it is the result of just doing the substitution and simplifying a bit with the given relations.

It shows that if you move k around with j, you will have a minimum absolute value for

nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2)

because x, y and nT are constant, as is α and k_0, so because the j^2 term will dominate r_2 will tend to be negative to compensate, and that allows you to get an idea of where k_0 is.

And if j=0, then z = (1+2α^2)k/(2α), so you have it explicitly.

The mathematics is what is commonly called elementary methods.

And I like simple.

I think about researchers around the world claiming to be working on the factoring problem who will say nothing about this research.

Weaklings.

Fakes.

That's me stepping back a bit. But I don't want these people staying in positions that they clearly are not filling later. So the warning to them is, yes, I want this research acknowledged before I fully force the situation, but when I do force it, if that is necessary, then the next problem I will solve will be making sure that none of them remain in the field as mathematicians or cryptographers, so they need to start thinking about what they will be doing for work, in the aftermath.

Or, show some goddamn sense, and just acknowledge the research now.

[A reply to someone who asked James whether or not he was thinking about doing some violent action.]

I'll admit that I'm still wary of the impact of a sudden change precipitated by me just factoring some really large number so I'd prefer buy-in from the cryptographic industry ahead of that event.

But make no mistake, if this impasse ends with me, say, factoring a large enough number to show this research must be viable, WITH the growing history now of an improper response from the cryptographic community then the likely impact will be a sharp loss of confidence in that industry.

But that industry would next be tasked with resolving the issue along with the high tech community so that secure transmissions could continue.

So the first major step would be just figuring out which of you are in on this cover-up or not, and even if you're not part of this particular cover-up, do you actually have real mathematical skills or are you a fake?

That could mean a snarl on looking for solutions, so yes, my putting out the theory now and talking about the research in-depth is methodical AND important.

Posters challenging me to just factor an RSA number are pushing the snarl, when if the research is viable the theory would show lots of indications that I could do so with plenty of time for proper industry action.

Given what I know about the current corruption in the mathematical community I'm not surprised by the behavior, but I'm still hopeful that there are some members of the cryptographic community who are legit.

Otherwise the snarl is what we will see down the line with the world—and I'm sure all major world leaders—facing the big issue of trying to figure out what to do when RSA encryption goes away, probably literally overnight, as it's potentially broken now by others, but we don't know that so it still works if only out of faith in it.

### Tuesday, February 26, 2008

## JSH: In the neighborhood

Oddly enough to me the most fascinating find from surrogate factoring which has created the means to end the impasse is a remarkably simple result that follows from a relatively simple equation:

x^2 = y^2 + nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2) - (k_0 + pj)pr_2

That is the equation that comes from letting 2αx = k + pr_2, and z = x + αk, when

z^2 = y^2 + nT

and considering k = k_0 + pj, to see how

nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2)

behaves as you increment or decrement k with j.

So actually I just kind of expanded out the traditional difference of squares.

Um, that's what they call thinking out of the box.

And you have trivially that as j increments OR decrements, r_2 will tend to be negative to compensate, so

nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2)

will have a minima and change around that value as j increases which is just an incredibly powerful result as it allows you to to get an idea of the value of z.

So the approach to the factoring problem is really tackling finding how to get z, when

z^2 = y^2 + nT

and all those variables are just helpers in that task.

You're just trying to get in the neighborhood.

And it can be shown that if x, y and z are rational

k^2 = (1 + α^2)^{-1}(nT) mod p

so you can go looking for z by looking for k, where you can get k's residue modulo p, an odd prime.

Qualifications are few. Yes, for a given choice of p, x, y and z rational may not exist such that all equations are satisfied but you can try different primes. Um, there are, after all, a LOT of primes.

So you have prime numbers as helpers that disappear after helping you to factor, and you have a surprisingly simple result with a parabolic minima, and you get quadratic residues, and it's the factoring problem and I've been talking about this latest research for days, and still math society waits…

Um, could REAL mathematicians wait?

Would Gauss or Euler or Fermat? Archimedes?

My place in history is secure even though I know a lot more than most of you clearly know so I also know that there may not be much history left! Not human history at least.

But not understanding is what this situation is all about, as some people didn't understand that lying about math would invite the retribution of the math because they didn't believe in mathematics itself.

The poor field was overrun by people who hate math but found a way to work the system by lying. That's all. Nothing more.

But without advancement in mathematics, humanity has no future, so the Universe will just kill off the species as no longer of further use.

By stopping mathematical progress, these people removed a key element in the purpose of the continued existence of the entire species so the clock is ticking down faster than any of you can imagine because you're too dumb to realize that if YOU lied and got things wrong, why couldn't others have?

Guess at how many years are left, and I'm sure you'll be wrong.

Yup. The test of humanity was a subtle one but it was very fair.

It was all about mathematical absolutes.

[A reply to someone who described what James had written as “meaningless garbage”.]

Actually it is easily derived.

Let z^2 = y^2 + nT, where T is the target to be factored.

Further let 2αx = k + p*r_2, where I use r_2 for historical reasons since the full theory also has an r_1, and where p is an odd prime of your choice.

Then you let z = x+αk, and substitute, and finally you let

k= k_0 + pj

where j is an integer.

As I explained in my initial post you get a remarkable result that k_0 will be near the maximum k such that abs(nT - (1+α^2)k^2) is a minimum, which you can prove rigorously with

x^2 = y^2 + nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2) - (k_0 + pj)pr_2

so the circle is complete.

It IS a simple result that has profound consequences, but we live in a complex world, so the debate continues as I face people who have learned to just fight for one more day.

Their strategy is always just to fight for one more day, fooling the world, and each day they keep people from the truth is a victory for them.

I am just one person fighting against a society around the world that is firmly entrenched that has betrayed the public trust.

At this point smarter people can exploit the mathematics but unfortunately I am sure that there are people who will try to hide exploits.

So yes, if say, a bank gets invaded by hackers who are breaking RSA at will, I fear that will be hidden. If you lose all your money as a result they will tell you it's your fault and you will not get a penny back.

If you protest you will be ignored.

And then you will understand how powerful they truly are.

I wish I knew a better way. Some way to save innocents from the fall-out.

But with a betrayal of trust on this scale I am at a loss for a better answer.

They will fail with a big collapse I fear, when they can no longer hide the security breaches. And can no longer explain away the collapses in security.

Florida in the United States lost power today. Is it yet another demonstration that will be explained away by powerful people fighting to keep their control? Or are the official explanations given correct?

I don't know.

My main task is to preserve civilization. IN order to do so I am empowered to sacrifice whatever needs to be lost. There are probably already lost.

Unheard. Unappreciated, except by me. I will honor their memory even if no one else understands.

x^2 = y^2 + nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2) - (k_0 + pj)pr_2

That is the equation that comes from letting 2αx = k + pr_2, and z = x + αk, when

z^2 = y^2 + nT

and considering k = k_0 + pj, to see how

nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2)

behaves as you increment or decrement k with j.

So actually I just kind of expanded out the traditional difference of squares.

Um, that's what they call thinking out of the box.

And you have trivially that as j increments OR decrements, r_2 will tend to be negative to compensate, so

nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2)

will have a minima and change around that value as j increases which is just an incredibly powerful result as it allows you to to get an idea of the value of z.

So the approach to the factoring problem is really tackling finding how to get z, when

z^2 = y^2 + nT

and all those variables are just helpers in that task.

You're just trying to get in the neighborhood.

And it can be shown that if x, y and z are rational

k^2 = (1 + α^2)^{-1}(nT) mod p

so you can go looking for z by looking for k, where you can get k's residue modulo p, an odd prime.

Qualifications are few. Yes, for a given choice of p, x, y and z rational may not exist such that all equations are satisfied but you can try different primes. Um, there are, after all, a LOT of primes.

So you have prime numbers as helpers that disappear after helping you to factor, and you have a surprisingly simple result with a parabolic minima, and you get quadratic residues, and it's the factoring problem and I've been talking about this latest research for days, and still math society waits…

Um, could REAL mathematicians wait?

Would Gauss or Euler or Fermat? Archimedes?

My place in history is secure even though I know a lot more than most of you clearly know so I also know that there may not be much history left! Not human history at least.

But not understanding is what this situation is all about, as some people didn't understand that lying about math would invite the retribution of the math because they didn't believe in mathematics itself.

The poor field was overrun by people who hate math but found a way to work the system by lying. That's all. Nothing more.

But without advancement in mathematics, humanity has no future, so the Universe will just kill off the species as no longer of further use.

By stopping mathematical progress, these people removed a key element in the purpose of the continued existence of the entire species so the clock is ticking down faster than any of you can imagine because you're too dumb to realize that if YOU lied and got things wrong, why couldn't others have?

Guess at how many years are left, and I'm sure you'll be wrong.

Yup. The test of humanity was a subtle one but it was very fair.

It was all about mathematical absolutes.

[A reply to someone who described what James had written as “meaningless garbage”.]

Actually it is easily derived.

Let z^2 = y^2 + nT, where T is the target to be factored.

Further let 2αx = k + p*r_2, where I use r_2 for historical reasons since the full theory also has an r_1, and where p is an odd prime of your choice.

Then you let z = x+αk, and substitute, and finally you let

k= k_0 + pj

where j is an integer.

As I explained in my initial post you get a remarkable result that k_0 will be near the maximum k such that abs(nT - (1+α^2)k^2) is a minimum, which you can prove rigorously with

x^2 = y^2 + nT - (1 + α^2)(k_0^2 + 2pjk_0 + p^2*j^2) - (k_0 + pj)pr_2

so the circle is complete.

It IS a simple result that has profound consequences, but we live in a complex world, so the debate continues as I face people who have learned to just fight for one more day.

Their strategy is always just to fight for one more day, fooling the world, and each day they keep people from the truth is a victory for them.

I am just one person fighting against a society around the world that is firmly entrenched that has betrayed the public trust.

At this point smarter people can exploit the mathematics but unfortunately I am sure that there are people who will try to hide exploits.

So yes, if say, a bank gets invaded by hackers who are breaking RSA at will, I fear that will be hidden. If you lose all your money as a result they will tell you it's your fault and you will not get a penny back.

If you protest you will be ignored.

And then you will understand how powerful they truly are.

I wish I knew a better way. Some way to save innocents from the fall-out.

But with a betrayal of trust on this scale I am at a loss for a better answer.

They will fail with a big collapse I fear, when they can no longer hide the security breaches. And can no longer explain away the collapses in security.

Florida in the United States lost power today. Is it yet another demonstration that will be explained away by powerful people fighting to keep their control? Or are the official explanations given correct?

I don't know.

My main task is to preserve civilization. IN order to do so I am empowered to sacrifice whatever needs to be lost. There are probably already lost.

Unheard. Unappreciated, except by me. I will honor their memory even if no one else understands.

### Monday, February 25, 2008

## JSH: Here comes alpha

Given a target composite T that you wish to factor, it can be shown that if you have

z^2 = y^2 + nT

where n is a non-zero integer, then there exists an integer k such that

k = 2a*z/(1+2a^2)

where 'a' is alpha, though I just use 'a' for text postings, and it is a non-zero integer.

Further z = x+ak, and 2ax = k.

And finally,

k^2 = (1+a^2)^{-1}(nT) mod p

where p is an odd prime.

Also k will be near the maximum value of k such that

abs(nT - (1+a^2)k^2)

is a MINIMUM, which is the powerful bit of mathematics which makes this very likely to be a solution to the factoring problem. That is the most crucial finding.

So if you've noticed me posting a lot on this subject you may have seen postings where I said z should be divisible by 3, that is because if alpha is coprime to 3, then 1+2a^2 is divisible by 3, so z must be, if that value of alpha works.

And it is about finding an alpha value that works as some value WILL work, if you have non-zero integers z and y such that z^2 = y^2 + nT.

So the first and most likely factor of z is 3, the next is 9, and the next is 19 when a=3, so yes, you can have z coprime to 3, followed by 33 when a=4, and 51 when a=5, and 73, when a=6.

Those must all be factors of z, where again

z^2 = y^2 + nT.

So alpha=1 is the most likely, and then you have other possible values for alpha since z is set for each non-trivial factorization so the question is finding alpha and k.

Finding k is about looking near the maximum value of k such that

abs(nT - (1+a^2)k^2)

is a minimum, and the most likely alpha is 1, but it may be others.

And you use

k^2 = (1+a^2)^{-1}(nT) mod p

where p is an odd prime of your choice, to get the residue of k modulo p, where you pick an odd prime and go looking.

Most likely for your prime, alpha=1, but it can equal the other values though the probability is less.

Those forced factors of z, again are

3, when a=1, 9, when a=2, and the next is 19 when a=3, followed by 33 when a=4, and 51 when a=5, and 73, when a=6.

So, for instance, if for your picked prime a=5 works, then z does not have to be divisible by 3, and it will have 73 as a factor as

k = 2a*z/(1+2a^2).

I went to the factoring problem to end an impasse where modern mathematicians around the world as it has taken a good bit of effort by these people from what I've seen, have been successfully blocking knowledge of major mathematical finds that overturn results that have a lot to do with their careers.

And they're blocking knowledge of certain key things, like that Andrew Wiles did not prove Fermat's Last Theorem, as the research that I have that does, also shows that a crucial error slipped into the mathematical field around the time of Dedekind—over a hundred years ago.

Those of you who know a bit about math know that an error can allow people to make "proofs" which are in fact, not mathematical proofs as mathematics does not tolerate error, so this error allows these people to create an ever growing body of useless and wrong research, indefinitely.

But they have to stop real researchers, so they have turned to various tactics as they claim they are keeping the field "pure", including interestingly enough casting doubt on mathematical proof itself so that people talk of delicate proofs.

As this answer to the factoring problem shows you, real mathematical proofs are not delicate.

These people are con artists who got into an area where they could lie with apparent impunity until they made a mistake, which was the introduction of a technique for information security based on factoring supposedly being a hard problem.

They have nowhere to go from here so do not expect them to tell the truth.

For them, now it's just about waiting until the world catches up, and they face the consequences of their actions.

z^2 = y^2 + nT

where n is a non-zero integer, then there exists an integer k such that

k = 2a*z/(1+2a^2)

where 'a' is alpha, though I just use 'a' for text postings, and it is a non-zero integer.

Further z = x+ak, and 2ax = k.

And finally,

k^2 = (1+a^2)^{-1}(nT) mod p

where p is an odd prime.

Also k will be near the maximum value of k such that

abs(nT - (1+a^2)k^2)

is a MINIMUM, which is the powerful bit of mathematics which makes this very likely to be a solution to the factoring problem. That is the most crucial finding.

So if you've noticed me posting a lot on this subject you may have seen postings where I said z should be divisible by 3, that is because if alpha is coprime to 3, then 1+2a^2 is divisible by 3, so z must be, if that value of alpha works.

And it is about finding an alpha value that works as some value WILL work, if you have non-zero integers z and y such that z^2 = y^2 + nT.

So the first and most likely factor of z is 3, the next is 9, and the next is 19 when a=3, so yes, you can have z coprime to 3, followed by 33 when a=4, and 51 when a=5, and 73, when a=6.

Those must all be factors of z, where again

z^2 = y^2 + nT.

So alpha=1 is the most likely, and then you have other possible values for alpha since z is set for each non-trivial factorization so the question is finding alpha and k.

Finding k is about looking near the maximum value of k such that

abs(nT - (1+a^2)k^2)

is a minimum, and the most likely alpha is 1, but it may be others.

And you use

k^2 = (1+a^2)^{-1}(nT) mod p

where p is an odd prime of your choice, to get the residue of k modulo p, where you pick an odd prime and go looking.

Most likely for your prime, alpha=1, but it can equal the other values though the probability is less.

Those forced factors of z, again are

3, when a=1, 9, when a=2, and the next is 19 when a=3, followed by 33 when a=4, and 51 when a=5, and 73, when a=6.

So, for instance, if for your picked prime a=5 works, then z does not have to be divisible by 3, and it will have 73 as a factor as

k = 2a*z/(1+2a^2).

I went to the factoring problem to end an impasse where modern mathematicians around the world as it has taken a good bit of effort by these people from what I've seen, have been successfully blocking knowledge of major mathematical finds that overturn results that have a lot to do with their careers.

And they're blocking knowledge of certain key things, like that Andrew Wiles did not prove Fermat's Last Theorem, as the research that I have that does, also shows that a crucial error slipped into the mathematical field around the time of Dedekind—over a hundred years ago.

Those of you who know a bit about math know that an error can allow people to make "proofs" which are in fact, not mathematical proofs as mathematics does not tolerate error, so this error allows these people to create an ever growing body of useless and wrong research, indefinitely.

But they have to stop real researchers, so they have turned to various tactics as they claim they are keeping the field "pure", including interestingly enough casting doubt on mathematical proof itself so that people talk of delicate proofs.

As this answer to the factoring problem shows you, real mathematical proofs are not delicate.

These people are con artists who got into an area where they could lie with apparent impunity until they made a mistake, which was the introduction of a technique for information security based on factoring supposedly being a hard problem.

They have nowhere to go from here so do not expect them to tell the truth.

For them, now it's just about waiting until the world catches up, and they face the consequences of their actions.

## JSH: All on my math blog

The full surrogate factoring theory is on my math blog.

Now I've been arguing still with posters who are playing the same games that worked to block the world from knowing that I found a proof of Fermat's Last Theorem--over five years ago.

And even a freaking math journal dying did not make a difference.

So I turned to the factoring problem.

Some of you are parasites. Like parasites in nature it is not in your nature to consider your own life when it comes to behaving as you are genetically or environmentally programmed.

You are human parasites so you behave as parasites and parasites can kill their host.

Here the host is human civilization as we currently know it.

Now the parasites would not be parasites if they were brilliant.

They established themselves in academic areas as the idea of "pure research" allowed them to get away with doing nothing of value if they gained critical mass so there is no telling how much of what we think of as valid knowledge is just parasitic waste product.

They just say that the research of their own is correct. Easy for them.

They needed to "publish or perish" to keep up their parasitic

activity.

Ok, so with the fate of the human race in the balance my job was to stop parasites who could block acceptance of a proof of Fermat's Last Theorem, of my prime counting function, of my definition of mathematical proof, of my basic logic axioms and just about anything else I came up with including my open source project and I think I even gave Google a business plan for YouTube and even that didn't matter.

So the factoring problem was it.

After arguing with myself for years about the ethical issues, while searching for the answer I concluded, especially as global warming grows as a problem, that the parasites were capable of driving the human race to extinction not because they want to, or because they're completely evil, but because they're stupid.

They are parasitic.

Do you think some math professor doing fake math really thinks he could end civilization as we know it?

No. No, but if you lose your family, or you are months away from a place where starvation is something you are facing as a reality when you're in a vibrant London today, or a healthy Amsterdam today when in a few months it can be like something out of a horror movie, the entire city, then once you are there, there is no going back, and there is no thinking to yourself that you should have listened.

Death is the greatest reality check of them all.

I can assure you of one thing, if what I call the Math Wars continue for much longer then many of you will learn that yes, there are such things as parasitic humans who have almost completely infested academia by your resignation as you face your own death, probably by starvation, though it may be by disease or lack of clean water.

We are so close to the brink here. And I would warn those that would exploit the solution of the factoring problem that they need to take stock and consider that maybe it's not such a good thing to steal a lot of money if their actions can just end everything as we know it.

I'm not sure how long parasitic math people can hold the line on this one.

But they sure are trying as hard as they worked to block my previous research.

So your life may be one of the sacrifices for the future of humanity.

But I had to make the calculation. And I decided that our entire species could be made extinct if the threat were not faced head on with force-on-force.

So I decided and here we are. You may die as a result, but consider if you lived so that everyone would die later in a world where parasites had simply removed the ability for people to solve problems for real, versus fantasy.

Even if it lasted hundreds of years before humanity finally just died out, everything before would have been for nothing. Our entire history, for nothing because at the end we couldn't handle the enemy from within.

So the real war has finally started. And if you die as a result, you have my apologies and my sympathy, but better you than everyone.

Now I've been arguing still with posters who are playing the same games that worked to block the world from knowing that I found a proof of Fermat's Last Theorem--over five years ago.

And even a freaking math journal dying did not make a difference.

So I turned to the factoring problem.

Some of you are parasites. Like parasites in nature it is not in your nature to consider your own life when it comes to behaving as you are genetically or environmentally programmed.

You are human parasites so you behave as parasites and parasites can kill their host.

Here the host is human civilization as we currently know it.

Now the parasites would not be parasites if they were brilliant.

They established themselves in academic areas as the idea of "pure research" allowed them to get away with doing nothing of value if they gained critical mass so there is no telling how much of what we think of as valid knowledge is just parasitic waste product.

They just say that the research of their own is correct. Easy for them.

They needed to "publish or perish" to keep up their parasitic

activity.

Ok, so with the fate of the human race in the balance my job was to stop parasites who could block acceptance of a proof of Fermat's Last Theorem, of my prime counting function, of my definition of mathematical proof, of my basic logic axioms and just about anything else I came up with including my open source project and I think I even gave Google a business plan for YouTube and even that didn't matter.

So the factoring problem was it.

After arguing with myself for years about the ethical issues, while searching for the answer I concluded, especially as global warming grows as a problem, that the parasites were capable of driving the human race to extinction not because they want to, or because they're completely evil, but because they're stupid.

They are parasitic.

Do you think some math professor doing fake math really thinks he could end civilization as we know it?

No. No, but if you lose your family, or you are months away from a place where starvation is something you are facing as a reality when you're in a vibrant London today, or a healthy Amsterdam today when in a few months it can be like something out of a horror movie, the entire city, then once you are there, there is no going back, and there is no thinking to yourself that you should have listened.

Death is the greatest reality check of them all.

I can assure you of one thing, if what I call the Math Wars continue for much longer then many of you will learn that yes, there are such things as parasitic humans who have almost completely infested academia by your resignation as you face your own death, probably by starvation, though it may be by disease or lack of clean water.

We are so close to the brink here. And I would warn those that would exploit the solution of the factoring problem that they need to take stock and consider that maybe it's not such a good thing to steal a lot of money if their actions can just end everything as we know it.

I'm not sure how long parasitic math people can hold the line on this one.

But they sure are trying as hard as they worked to block my previous research.

So your life may be one of the sacrifices for the future of humanity.

But I had to make the calculation. And I decided that our entire species could be made extinct if the threat were not faced head on with force-on-force.

So I decided and here we are. You may die as a result, but consider if you lived so that everyone would die later in a world where parasites had simply removed the ability for people to solve problems for real, versus fantasy.

Even if it lasted hundreds of years before humanity finally just died out, everything before would have been for nothing. Our entire history, for nothing because at the end we couldn't handle the enemy from within.

So the real war has finally started. And if you die as a result, you have my apologies and my sympathy, but better you than everyone.

### Saturday, February 23, 2008

## JSH: How they do it

To me it's still rather neat to find this surprisingly useful relationship from considering

abs(nT - 2k^2)

and the maximum k for which that value is a minimum, when T is an odd composite to factor, and n is just there to force nT mod 3 = 2, so you can use 5, when T mod 3 = 1, but 1 otherwise.

Then that k is at or near a value such k is a solution when z = 3k/2, and

z^2 = y^2 + nT

and you have a non-trivial factorization of nT.

Now that follows from doing something out of the box as I deliberately looked at

2x = k mod p

for quite some time just so that I could complete a square, as I was speculating about factoring T by using the factorization of some other number.

So getting the full result is just about using

2x = k + pr

where r is just some integer and substituting with z = x + k, into

z^2 = y^2 + nT

and doing some basic algebraic analysis and I explain all of that to emphasize the simplicity of the approach, and many of you can do it yourself to verify or read my other recent posts to see more detail.

And it's a fascinating result for many reasons, but one of them is that the p kind of vanishes after helping you factor by helping you find the correct k.

I can also show that k^2 = 2^{-1}(nT) mod p, so you can just go looking for large primes—as the bigger the prime the quicker you can factor—when you have a large composite T, so you actually get to just go find some primes and know about where to look and can factor.

So that should be a big deal as a nice bit of interesting mathematics that could have impact on the use of RSA encryption and it's just a neat result, so why am I still the "crackpot" on newsgroups instead of celebrated in the mainstream?

Well I'm looking at posts in reply to me and not seeing much new which is why I wanted to explain to you how they do it: how they keep the truth from being mainstreamed.

I have other mathematical results and watched the same process with them.

That process is to deny, mostly ignore, or claim ignorance of the result or of the behavior around the result.

So some posters will keeps posting nastily in reply and just claim I'm wrong, while others will post puzzlement that I'm even posting! While others will post puzzlement that anything I have ever said was ever ignored as they claim none of it was and that in fact I get plenty of attention so why am I complaining.

But they'll ignore any current result. If pressed they will simply quit replying.

Years ago when I first faced this process, yes, I went off Usenet, and got a paper published. I'm sitting back waiting for math society to acknowledge that remarkable result—but monitoring Usenet just to see what happened—and some poster posts that I'm published on the sci.math newsgroup and the group erupted in fury.

Never paused for a moment to consider that maybe publication meant something.

There is what people say they believe and there is what they demonstrate they truly believe. Publication. Hmmm…

Now you can see how they react with the factoring problem.

Yes, I've said for some time that I had solved it only to be wrong, but I know this process better than you do, and my strategy is based on game theory.

And you can see what I'm up against if you understand that simple approach I outlined before about using abs(nT - 2k^2) and understand it, as well as the implications, and see how math society is STILL to this point reacting.

Lying is as old as humanity. People lie to get things they would not get otherwise.

Some of you may be going to math classes to listen to professors who would not be there if they told the truth. It's that simple. It can be easy to talk about the fate of the human race and the importance of knowledge and progress in the abstract, but if you're some middle-aged man with a mortgage, a wife who thinks you're brilliant, and other perks that may come with being a math professor (yes there are some perks for some maybe not many but some) considering accepting not being so brilliant and losing what you have, then lying can seem to be just about survival.

Perspective is an amazing thing.

Some of these people may figure that humanity is such a big thing that there's no way it can really matter if they stop intellectual progress in mathematics for a while. So they did. They stopped most progress in "pure math" areas for the entire human race across the planet.

So I went to the factoring problem.

Now then, yes, humanity is kind of big to us, and it can seem easy to think that getting your little piece today is worth blocking its progress for a little while, especially to stop some annoying guy—just some guy after all—who keeps going on and on about his mathematical research.

Because history makes the legends—so I can't be one to you now—so it's later that students will read about you and find it incomprehensible that you could have even paused with the fate of your own species in the balance, and what could have been so important to you that you'd actually deny progress for people who were just lying?

But they would also know how it's in the balance. Some of them might contemplate not getting to be born because of what you are doing now—if you weren't stopped.

But they aren't in your shoes now. Perspective.

Legacy is a word that gets tossed around, but thinking that maybe down the line your legacy can be that of THOSE people, who didn't do the right thing, who held on even when it was clear that they were wrong, and broken later, could only fumble out rationalizations or apologies and accept their branding for life, is an exercise for those who aren't thinking about their bills and just trying to have a life.

If you were brilliant you wouldn't be in this situation.

Make no mistake, the world is not a nice place when you get on the outside and are looked at as a renegade versus being one of us.

You are inside now, and if you are a math professor, then you are very inside, but think about what happens if you keep up this nonsense and you are completely out.

I'm a problem solver. I brainstormed my way through some important and difficult math problems, got the answers, and found a society that couldn't or wouldn't live up to expectations so I am working on solving that problem as well.

My mistakes are many, but I own up to them. I have been wrong many times before, said things I know I'll regret later, and often wondered how this situation is even possible—until I remember—perspective.

No criminal ever thought first, long and hard, about getting caught, enough to not do the crimes.

If they had, then they wouldn't be criminals, now would they?

abs(nT - 2k^2)

and the maximum k for which that value is a minimum, when T is an odd composite to factor, and n is just there to force nT mod 3 = 2, so you can use 5, when T mod 3 = 1, but 1 otherwise.

Then that k is at or near a value such k is a solution when z = 3k/2, and

z^2 = y^2 + nT

and you have a non-trivial factorization of nT.

Now that follows from doing something out of the box as I deliberately looked at

2x = k mod p

for quite some time just so that I could complete a square, as I was speculating about factoring T by using the factorization of some other number.

So getting the full result is just about using

2x = k + pr

where r is just some integer and substituting with z = x + k, into

z^2 = y^2 + nT

and doing some basic algebraic analysis and I explain all of that to emphasize the simplicity of the approach, and many of you can do it yourself to verify or read my other recent posts to see more detail.

And it's a fascinating result for many reasons, but one of them is that the p kind of vanishes after helping you factor by helping you find the correct k.

I can also show that k^2 = 2^{-1}(nT) mod p, so you can just go looking for large primes—as the bigger the prime the quicker you can factor—when you have a large composite T, so you actually get to just go find some primes and know about where to look and can factor.

So that should be a big deal as a nice bit of interesting mathematics that could have impact on the use of RSA encryption and it's just a neat result, so why am I still the "crackpot" on newsgroups instead of celebrated in the mainstream?

Well I'm looking at posts in reply to me and not seeing much new which is why I wanted to explain to you how they do it: how they keep the truth from being mainstreamed.

I have other mathematical results and watched the same process with them.

That process is to deny, mostly ignore, or claim ignorance of the result or of the behavior around the result.

So some posters will keeps posting nastily in reply and just claim I'm wrong, while others will post puzzlement that I'm even posting! While others will post puzzlement that anything I have ever said was ever ignored as they claim none of it was and that in fact I get plenty of attention so why am I complaining.

But they'll ignore any current result. If pressed they will simply quit replying.

Years ago when I first faced this process, yes, I went off Usenet, and got a paper published. I'm sitting back waiting for math society to acknowledge that remarkable result—but monitoring Usenet just to see what happened—and some poster posts that I'm published on the sci.math newsgroup and the group erupted in fury.

Never paused for a moment to consider that maybe publication meant something.

There is what people say they believe and there is what they demonstrate they truly believe. Publication. Hmmm…

Now you can see how they react with the factoring problem.

Yes, I've said for some time that I had solved it only to be wrong, but I know this process better than you do, and my strategy is based on game theory.

And you can see what I'm up against if you understand that simple approach I outlined before about using abs(nT - 2k^2) and understand it, as well as the implications, and see how math society is STILL to this point reacting.

Lying is as old as humanity. People lie to get things they would not get otherwise.

Some of you may be going to math classes to listen to professors who would not be there if they told the truth. It's that simple. It can be easy to talk about the fate of the human race and the importance of knowledge and progress in the abstract, but if you're some middle-aged man with a mortgage, a wife who thinks you're brilliant, and other perks that may come with being a math professor (yes there are some perks for some maybe not many but some) considering accepting not being so brilliant and losing what you have, then lying can seem to be just about survival.

Perspective is an amazing thing.

Some of these people may figure that humanity is such a big thing that there's no way it can really matter if they stop intellectual progress in mathematics for a while. So they did. They stopped most progress in "pure math" areas for the entire human race across the planet.

So I went to the factoring problem.

Now then, yes, humanity is kind of big to us, and it can seem easy to think that getting your little piece today is worth blocking its progress for a little while, especially to stop some annoying guy—just some guy after all—who keeps going on and on about his mathematical research.

Because history makes the legends—so I can't be one to you now—so it's later that students will read about you and find it incomprehensible that you could have even paused with the fate of your own species in the balance, and what could have been so important to you that you'd actually deny progress for people who were just lying?

But they would also know how it's in the balance. Some of them might contemplate not getting to be born because of what you are doing now—if you weren't stopped.

But they aren't in your shoes now. Perspective.

Legacy is a word that gets tossed around, but thinking that maybe down the line your legacy can be that of THOSE people, who didn't do the right thing, who held on even when it was clear that they were wrong, and broken later, could only fumble out rationalizations or apologies and accept their branding for life, is an exercise for those who aren't thinking about their bills and just trying to have a life.

If you were brilliant you wouldn't be in this situation.

Make no mistake, the world is not a nice place when you get on the outside and are looked at as a renegade versus being one of us.

You are inside now, and if you are a math professor, then you are very inside, but think about what happens if you keep up this nonsense and you are completely out.

I'm a problem solver. I brainstormed my way through some important and difficult math problems, got the answers, and found a society that couldn't or wouldn't live up to expectations so I am working on solving that problem as well.

My mistakes are many, but I own up to them. I have been wrong many times before, said things I know I'll regret later, and often wondered how this situation is even possible—until I remember—perspective.

No criminal ever thought first, long and hard, about getting caught, enough to not do the crimes.

If they had, then they wouldn't be criminals, now would they?

## JSH: Sorry, but exasperated

It's been over five years since I found a proof of Fermat's Last Theorem.

I still believed enough in modern math society that I questioned and questioned and questioned my own result as people fought successfully against it being accepted.

I even kind of wondered still when I pulled out a piece of it and got that published, only to have math society fail completely when the math journal went against formal peer review, pulled my paper and later died.

You people may have heard the story but may not have realized that I have been right, dealing with people who I continually saw shifting their tactics as I explained as they fought a political battle to make sure no one believed me.

One thing that kept me from simply giving up was that I knew they wanted it. They begged for it, literally.

After all, if I weren't around to champion my ideas then they could keep them suppressed.

Then Andrew Wiles could keep credit for something he didn't do.

And undergrads could keep getting taught crap math which would never work not because it is "pure" but because it's wrong, but not easily testable in a way that can show it's wrong.

The perfect trap.

The way the fight has gone against my research has evolved as my strategies evolved and as the people doing it had to handle my moves in other areas, as I looked desperately for ANY way to prove that I was right and that these people were deliberately lying.

They turned success into a perception of failure.

I've said it's like winning the Olympics and being booed and the gold medal going to someone who didn't even run the race.

They turned everything on its head.

So I turned to the factoring problem.

It still gets to me though, after so many years of dealing with these people to see posters STILL trying the same games, the same ways to distract and deny with an argument so simple it stunned me.

Who knew? Turns out there's this neat thing with abs(nT - 2k^2) where you look at a simple integer minima with k maximal.

Not even I thought the entire world could turn on a result that simple, but turn it will.

Blocking "pure math" is one thing but posters fighting now are trying to stop knowledge of a result that can mean your actual physical life could be in danger, or your financials.

Lying here can mean the ruin of some of you, and isn't it ironic, don't you think?

They will try. As what have the got left now?

Their battle was an all or nothing war against the latest (maybe the last) major discoverer.

They have nothing left to do but fight until the bitter end.

There have only been a handful of people like me in all of human history.

And I wish that I had not been born to face this mess of what humanity has become.

I still believed enough in modern math society that I questioned and questioned and questioned my own result as people fought successfully against it being accepted.

I even kind of wondered still when I pulled out a piece of it and got that published, only to have math society fail completely when the math journal went against formal peer review, pulled my paper and later died.

You people may have heard the story but may not have realized that I have been right, dealing with people who I continually saw shifting their tactics as I explained as they fought a political battle to make sure no one believed me.

One thing that kept me from simply giving up was that I knew they wanted it. They begged for it, literally.

After all, if I weren't around to champion my ideas then they could keep them suppressed.

Then Andrew Wiles could keep credit for something he didn't do.

And undergrads could keep getting taught crap math which would never work not because it is "pure" but because it's wrong, but not easily testable in a way that can show it's wrong.

The perfect trap.

The way the fight has gone against my research has evolved as my strategies evolved and as the people doing it had to handle my moves in other areas, as I looked desperately for ANY way to prove that I was right and that these people were deliberately lying.

They turned success into a perception of failure.

I've said it's like winning the Olympics and being booed and the gold medal going to someone who didn't even run the race.

They turned everything on its head.

So I turned to the factoring problem.

It still gets to me though, after so many years of dealing with these people to see posters STILL trying the same games, the same ways to distract and deny with an argument so simple it stunned me.

Who knew? Turns out there's this neat thing with abs(nT - 2k^2) where you look at a simple integer minima with k maximal.

Not even I thought the entire world could turn on a result that simple, but turn it will.

Blocking "pure math" is one thing but posters fighting now are trying to stop knowledge of a result that can mean your actual physical life could be in danger, or your financials.

Lying here can mean the ruin of some of you, and isn't it ironic, don't you think?

They will try. As what have the got left now?

Their battle was an all or nothing war against the latest (maybe the last) major discoverer.

They have nothing left to do but fight until the bitter end.

There have only been a handful of people like me in all of human history.

And I wish that I had not been born to face this mess of what humanity has become.

## JSH: So tired

You people have no clue the kind of energy it takes out of you to figure out a major discovery or how much more tiring it is when nasty people dismiss the math.

I'm so tired today not so much from finding the result but from the sapping effect of reading posts by people who clearly despise mathematics who get away with it.

How can they?

Aren't any of you excited by the factoring problem?

Yes, I've made lots of mistakes so many of you probably just tune me out, but do you all? Are you all immune to a brilliant but succinct mathematical argument unless someone else TELLS you it is?

Then WHY ARE YOU IN THE MATH FIELD?

That's what keeps going through my mind. How did our world get so pathetic and lost that you people are it in mathematics.

That so many people get away with pretending to be mathematicians.

How did humanity so horribly lose its way?

How can anyone hope? I keep worrying that it is game over and our species has nowhere to go but extinction as it has lost the ability to know the truth, and cherish it.

I'm so tired today not so much from finding the result but from the sapping effect of reading posts by people who clearly despise mathematics who get away with it.

How can they?

Aren't any of you excited by the factoring problem?

Yes, I've made lots of mistakes so many of you probably just tune me out, but do you all? Are you all immune to a brilliant but succinct mathematical argument unless someone else TELLS you it is?

Then WHY ARE YOU IN THE MATH FIELD?

That's what keeps going through my mind. How did our world get so pathetic and lost that you people are it in mathematics.

That so many people get away with pretending to be mathematicians.

How did humanity so horribly lose its way?

How can anyone hope? I keep worrying that it is game over and our species has nowhere to go but extinction as it has lost the ability to know the truth, and cherish it.

## JSH: Test factorization

I've modified one of my existing programs to start testing out the latest surrogate factoring research though I haven't yet optimized it, so it kind of dumbly just looks for solutions around k approximately equal sqrt(nT/2) where n=1 if T mod 3 = 2, and n=5, if T mod 3 = 1.

Here's an example factorization:

T = 1342517983, k = 58480. surrogate = 127230885, which factors as

(3^3)(5)(449)(2099)

and T factors as (27893)(48131). The prime factors of the surrogate are of interest here and since T mod 3 = 1, the program multiplies it by 5, so

k^2 = 2^{-1}(5T) mod p

where you can check it for each prime. I haven't bothered to check.

Because the program is dumb, it took 183 checks of k's looping up from k approximately equals sqrt(5T/2), skipping over odd k's or k's divisible by 3.

Notice that k/2p approximately equals 14 using the largest prime, so you'd have a roughly a 1/14 chance of finding a solution, if you did it the smarter way, but that gave a good enough chance that even the dumb way stumbled across the factors.

It's not a complicated idea here, which is why it's amazing to me there are still people trying to argue over some rather basic algebra.

It just so happens that if you let k = 2x, and z = x+k, when

z^2 = y^2 + nT

then the maximum k that will give the minimum value for abs(nT - 2k^2) will tend to be close to the correct k, which must exist if z is divisible by 3 because

z = x + k = x + 2x = 3x.

Figuring that out just requires using

2x = k + pr

where p is some prime and r is an integer, and the substituting out z, with z = x+k, to get

if you substitute out z and simplify a bit you have

x^2 = y^2 + nT - (2xk + k^2)

so you can substitute out 2x, and get

x^2 = y^2 + nT - 2k^2 - kpr

and now let k_0 be the value for which r=0, so you can let

k = k_0 + 2pj

where j is an integer and substitute, and you have

x^2 = y^2 + nT - 2(k_0^2 + 4pjk_0 + 4p^2j^2) - (k_0 + 2pj)pr

and x, y, nT, k_0 and p are all constant, so as j varies, the j^2 term will dominate and the r variable will tend to be negative to counterbalance it.

If you need it all multiplied out to help you with this basic point:

x^2 = y^2 + nT - 2k_0^2 - 8pjk_0 - 8p^2j^2 - (k_0 + 2pj)pr

where with k_0 positive (as why have it negative?), you'll notice that while

k_0 <2pj

the negativity of 8p^2j^2 can't be overridden by -8pjk_0 no matter what the sign of j, but y^2 + nT - 2k_0^2 is constant as is x^2, so r must be negative to compensate until k_0 = 2pj, which is when k=0 anyway.

So it's trivial mathematics that k_0 will tend to be near the correct answer for k, when it is the maximum value such that abs(nT - 2k^2) is a minimum.

That amazing bit of mathematics puts the factoring problem within reach, just like that just because the j^2 is always positive.

Trivial algebra gives you the range as k should be equal to or greater than k_0, and j should be negative and greater than -k/2p.

Figuring out that k^2 = 2^{-1}(nT) mod p, is a little more complicated but if you were paying attention when I was babbling on about factors mod p, I explained it exhaustively and ad nauseum.

So, oddly enough, to tackle a composite T, you just need to get a a prime for which k exists that makes it very likely that you will find k quickly.

And it's all trivial algebra.

Now if you people wish to argue on still and wait until I or someone else is motivated to fully implement the trivial algebra, then fine. But don't come crying later when I say you people don't really know math, as then you clearly don't.

Easy algebra ignored when it's the factoring problem does not make you brilliant.

It does still annoy me and I still wonder how I let some of you bother me, that you can pretend to give a damn about mathematics and come out with sophistry to attack a beautiful and simple argument, proving how much you hate math, but having the gall to keep at it as if you can just fool people one more day, that's all that matters.

I think some of you every day you post arguing with me just tell yourself, to just try to get people to believe wrong things mathematically one more day, and you win, as you make humanity as a whole lose. One more day yesterday you people won.

Did you win today? Is humanity still being fooled by you?

[A reply to someone who asked which constraint should one use to pick

Oh please. Like what you do matters.

If this result is correct then someone in the world will pick it up.

Your input is irrelevant as is the input of everyone else on these groups.

I'm mostly just talking to myself anyway.

When the real storm hits, your voice will disappear as nothing you will say at that point will make any difference at all.

I'm kind of just appreciating the calm before the storm, before the world knows fully who I am, and that I am the next great discoverer, of a long line of discoverers.

That I am the next legend—living, breathing and solving mega problems in the here and now.

Not just some person to be read about, but someone that can be asked important questions, which is what I truly dread. When people get smart enough to ask me the real questions.

Here's an example factorization:

T = 1342517983, k = 58480. surrogate = 127230885, which factors as

(3^3)(5)(449)(2099)

and T factors as (27893)(48131). The prime factors of the surrogate are of interest here and since T mod 3 = 1, the program multiplies it by 5, so

k^2 = 2^{-1}(5T) mod p

where you can check it for each prime. I haven't bothered to check.

Because the program is dumb, it took 183 checks of k's looping up from k approximately equals sqrt(5T/2), skipping over odd k's or k's divisible by 3.

Notice that k/2p approximately equals 14 using the largest prime, so you'd have a roughly a 1/14 chance of finding a solution, if you did it the smarter way, but that gave a good enough chance that even the dumb way stumbled across the factors.

It's not a complicated idea here, which is why it's amazing to me there are still people trying to argue over some rather basic algebra.

It just so happens that if you let k = 2x, and z = x+k, when

z^2 = y^2 + nT

then the maximum k that will give the minimum value for abs(nT - 2k^2) will tend to be close to the correct k, which must exist if z is divisible by 3 because

z = x + k = x + 2x = 3x.

Figuring that out just requires using

2x = k + pr

where p is some prime and r is an integer, and the substituting out z, with z = x+k, to get

if you substitute out z and simplify a bit you have

x^2 = y^2 + nT - (2xk + k^2)

so you can substitute out 2x, and get

x^2 = y^2 + nT - 2k^2 - kpr

and now let k_0 be the value for which r=0, so you can let

k = k_0 + 2pj

where j is an integer and substitute, and you have

x^2 = y^2 + nT - 2(k_0^2 + 4pjk_0 + 4p^2j^2) - (k_0 + 2pj)pr

and x, y, nT, k_0 and p are all constant, so as j varies, the j^2 term will dominate and the r variable will tend to be negative to counterbalance it.

If you need it all multiplied out to help you with this basic point:

x^2 = y^2 + nT - 2k_0^2 - 8pjk_0 - 8p^2j^2 - (k_0 + 2pj)pr

where with k_0 positive (as why have it negative?), you'll notice that while

k_0 <2pj

the negativity of 8p^2j^2 can't be overridden by -8pjk_0 no matter what the sign of j, but y^2 + nT - 2k_0^2 is constant as is x^2, so r must be negative to compensate until k_0 = 2pj, which is when k=0 anyway.

So it's trivial mathematics that k_0 will tend to be near the correct answer for k, when it is the maximum value such that abs(nT - 2k^2) is a minimum.

That amazing bit of mathematics puts the factoring problem within reach, just like that just because the j^2 is always positive.

Trivial algebra gives you the range as k should be equal to or greater than k_0, and j should be negative and greater than -k/2p.

Figuring out that k^2 = 2^{-1}(nT) mod p, is a little more complicated but if you were paying attention when I was babbling on about factors mod p, I explained it exhaustively and ad nauseum.

So, oddly enough, to tackle a composite T, you just need to get a a prime for which k exists that makes it very likely that you will find k quickly.

And it's all trivial algebra.

Now if you people wish to argue on still and wait until I or someone else is motivated to fully implement the trivial algebra, then fine. But don't come crying later when I say you people don't really know math, as then you clearly don't.

Easy algebra ignored when it's the factoring problem does not make you brilliant.

It does still annoy me and I still wonder how I let some of you bother me, that you can pretend to give a damn about mathematics and come out with sophistry to attack a beautiful and simple argument, proving how much you hate math, but having the gall to keep at it as if you can just fool people one more day, that's all that matters.

I think some of you every day you post arguing with me just tell yourself, to just try to get people to believe wrong things mathematically one more day, and you win, as you make humanity as a whole lose. One more day yesterday you people won.

Did you win today? Is humanity still being fooled by you?

[A reply to someone who asked which constraint should one use to pick

*k*when programming.]Oh please. Like what you do matters.

If this result is correct then someone in the world will pick it up.

Your input is irrelevant as is the input of everyone else on these groups.

I'm mostly just talking to myself anyway.

When the real storm hits, your voice will disappear as nothing you will say at that point will make any difference at all.

I'm kind of just appreciating the calm before the storm, before the world knows fully who I am, and that I am the next great discoverer, of a long line of discoverers.

That I am the next legend—living, breathing and solving mega problems in the here and now.

Not just some person to be read about, but someone that can be asked important questions, which is what I truly dread. When people get smart enough to ask me the real questions.

### Friday, February 22, 2008

## JSH: Fairly straightforward

So yeah, some guy going on and on about mathematical arguments that are wrong can be annoying, but what if he gets something right?

Then who cares? Right? If you care about mathematics for real then you take the good, and you take the bad and just accept what has to be true.

And THAT is what was so devastating for me, years ago, when I realized that there are so many people in the mathematical community who don't think that way.

They pick and choose.

And they think if they don't like a person they can justify ignoring what the person discovers because of what that person can get from those discoveries.

So they care more about the gain.

There is no way that math people give a damn if I get famous or make a lot of money from my mathematical discoveries if they aren't obsessed over getting famous and making a lot of money—probably figuring that it's just something they won't get, but maybe…

If they just care about the mathematics, then who cares what I get?

If money means nothing, and if fame means nothing, and the mathematics means EVERYTHING then all that matters is getting the knowledge and marveling over the mathematical reality.

But you people pick and choose, now don't you?

And you do so calculating what you think I'll get based on how you react.

Ergo, you don't really care about the mathematical truth.

You cannot.

If you did then you would behave as people who do.

As Forrest Gump might say, people are as people do.

I feel like Forrest Gump—the guy who did what a group of people didn't think was possible but then they showed that they didn't give a damn about their own area, but only what they thought it could give them.

Intelligence is as intelligence does.

Loving mathematics is about loving what mathematics is.

Not what you wish it were.

x^2 = y^2 + T - 2(k^2 + 12j + 36j^2) - 3(k+6j)r

That's a mathematical equation. It just is. What it tells is about mathematical truth.

If x, y, T and k are constant, then as j varies, r must vary to counterbalance it and it will tend to be negative as j increases either positively or negatively.

That can hurt though as it shows a way to factor when you generalize to p odd prime.

Using just 2x = k + pr, and z^2 = y^2 + nT and z = x + k.

Beautiful mathematics in its conciseness but possibly repulsive to some of you because you see it as validating me and my approaches, and what I call Extreme Mathematics, and arguing with people and getting a lot wrong just for WHAT YOU GET RIGHT.

And hating the process and hating a person can be everything to you because you do not love the mathematical truth, so why later should you be allowed to stay in the mathematical field and claim to be a mathematician?

Why?

Because people like you and feel sorry for you?

Because even if you can't do real mathematics you really, really, really want to believe that you can?

[A reply to someone who called James “narcissist”.]

So? Even if I were, so? I don't go around trying to find people to verbally assault claiming it's their fault. You do.

I work at hard math problems.

I get a lot wrong.

But I admit it. I talk about the process, about brainstorming.

And I know that it can take a lot out of you to do the effort to get something right.

Then I consider creatures like yourself who think that it is my job to just sit back and be nice when I get it right and think about how much damage someone like you can do.

What if instead I try to make it harder for your type to operate?

Why shouldn't I?

You made your bets, right? You put yourself out there, made your posts and that is about what you committed yourself to doing.

Why shouldn't I make certain that you get the full consequences based on reality?

Nothing any of you do here is truly anonymous.

All of you as wanted will be tracked down and known.

To me justifying my support of that activity is all about how much time I've spent thinking about the kind of people who make an effort to try and find other people as prey.

I've pondered those who look to try and find vulnerable people that they think they can feed on in some way, so yeah, to such parasites a guy they think is just giving wrong answers all the time when math society says he's wrong could be one of these vulnerable humans.

So I studied that behavior. Contemplated it. Pondered what it meant about the creatures who displayed it.

But what if he's a great discoverer when no one really knows what one is like as it has been so long since one was here and none have been around in the Internet age when you could talk to one repeatedly in a direct way?

Why if you got it so wrong should I not let you feel the full consequence of that failure?

The answer is, I should not.

It is not in my nature to do so, so it must be then that you will discover reality is not as simple as you thought, and that human prey can turn out to be more than you ever thought possible because being a parasite is about what was.

While I am about the future and what will be.

No major discover has emerged before in the Internet age.

No one has been around for you to know exactly what a person like me is like, so you have no clue what is coming.

The simplest way to describe it, is change.

Then who cares? Right? If you care about mathematics for real then you take the good, and you take the bad and just accept what has to be true.

And THAT is what was so devastating for me, years ago, when I realized that there are so many people in the mathematical community who don't think that way.

They pick and choose.

And they think if they don't like a person they can justify ignoring what the person discovers because of what that person can get from those discoveries.

So they care more about the gain.

There is no way that math people give a damn if I get famous or make a lot of money from my mathematical discoveries if they aren't obsessed over getting famous and making a lot of money—probably figuring that it's just something they won't get, but maybe…

If they just care about the mathematics, then who cares what I get?

If money means nothing, and if fame means nothing, and the mathematics means EVERYTHING then all that matters is getting the knowledge and marveling over the mathematical reality.

But you people pick and choose, now don't you?

And you do so calculating what you think I'll get based on how you react.

Ergo, you don't really care about the mathematical truth.

You cannot.

If you did then you would behave as people who do.

As Forrest Gump might say, people are as people do.

I feel like Forrest Gump—the guy who did what a group of people didn't think was possible but then they showed that they didn't give a damn about their own area, but only what they thought it could give them.

Intelligence is as intelligence does.

Loving mathematics is about loving what mathematics is.

Not what you wish it were.

x^2 = y^2 + T - 2(k^2 + 12j + 36j^2) - 3(k+6j)r

That's a mathematical equation. It just is. What it tells is about mathematical truth.

If x, y, T and k are constant, then as j varies, r must vary to counterbalance it and it will tend to be negative as j increases either positively or negatively.

That can hurt though as it shows a way to factor when you generalize to p odd prime.

Using just 2x = k + pr, and z^2 = y^2 + nT and z = x + k.

Beautiful mathematics in its conciseness but possibly repulsive to some of you because you see it as validating me and my approaches, and what I call Extreme Mathematics, and arguing with people and getting a lot wrong just for WHAT YOU GET RIGHT.

And hating the process and hating a person can be everything to you because you do not love the mathematical truth, so why later should you be allowed to stay in the mathematical field and claim to be a mathematician?

Why?

Because people like you and feel sorry for you?

Because even if you can't do real mathematics you really, really, really want to believe that you can?

[A reply to someone who called James “narcissist”.]

So? Even if I were, so? I don't go around trying to find people to verbally assault claiming it's their fault. You do.

I work at hard math problems.

I get a lot wrong.

But I admit it. I talk about the process, about brainstorming.

And I know that it can take a lot out of you to do the effort to get something right.

Then I consider creatures like yourself who think that it is my job to just sit back and be nice when I get it right and think about how much damage someone like you can do.

What if instead I try to make it harder for your type to operate?

Why shouldn't I?

You made your bets, right? You put yourself out there, made your posts and that is about what you committed yourself to doing.

Why shouldn't I make certain that you get the full consequences based on reality?

Nothing any of you do here is truly anonymous.

All of you as wanted will be tracked down and known.

To me justifying my support of that activity is all about how much time I've spent thinking about the kind of people who make an effort to try and find other people as prey.

I've pondered those who look to try and find vulnerable people that they think they can feed on in some way, so yeah, to such parasites a guy they think is just giving wrong answers all the time when math society says he's wrong could be one of these vulnerable humans.

So I studied that behavior. Contemplated it. Pondered what it meant about the creatures who displayed it.

But what if he's a great discoverer when no one really knows what one is like as it has been so long since one was here and none have been around in the Internet age when you could talk to one repeatedly in a direct way?

Why if you got it so wrong should I not let you feel the full consequence of that failure?

The answer is, I should not.

It is not in my nature to do so, so it must be then that you will discover reality is not as simple as you thought, and that human prey can turn out to be more than you ever thought possible because being a parasite is about what was.

While I am about the future and what will be.

No major discover has emerged before in the Internet age.

No one has been around for you to know exactly what a person like me is like, so you have no clue what is coming.

The simplest way to describe it, is change.

### Thursday, February 21, 2008

## JSH: Finding k

Surprising answer with surrogate factoring that focuses on finding k, and leverages a rather intriguingly simple little result to factor.

As consider

2x = k + 3r

when

z^2 = y^2 + T

where T is the target to be factored, is odd and coprime to 3, and T mod 3 = 2, as then z must have 3 as a factor, so

z = x+k

gives

x^2 + 2xk + k^2 = y^2 + T

which is x^2 = y^2 + T - 2xk - k^2, and I can substitute out 2x, to get

x^2 = y^2 + T - 2k^2 - 3kr

and that's where a nifty thing pops in, as, you want r=0, but in general, r will be NEGATIVE if you start with the optimal k when r=0 and move about modulo 6, as that k will be even. That's because you'd have

x^2 = y^2 + T - 2(k+6j)^2 - 3(k+6j)r

and if you have positive k (no reason to use negative) and try to move with positive j, then r will be negative, and even if you move with negative j, the 36j^2 term will tend to dominate, forcing r to be negative to compensate.

So r = 0 should be near the value at which abs(T-2k^2) is a minimum.

Trouble is, if you continue the analysis you find that k at that point is the minimum that might work—remember k is positive—but the actual k MUST be within k/6 steps from that value.

But it gives you a sense of what is possible, just with p=3.

I generalized to p odd prime though, but found that it's still important to have z with 3 as a factor, but then you have as a crucial requirement:

k^2 = (nT)(2)^{-1} mod p

so you need a prime for which k exists, and then you find a maximal k modulo that prime, as the same argument above works, except now you'd have

2x = k + pr

and you have a solution within k/(2p) steps from the maximal k.

If T mod 3 = 2, then you'd use n=1, else you'd use n=5 or maybe 2, I'm still not sure, to force nT mod 3 = 2, as there is a crucial requirement that

z = 3x

so z has to have 3 as a factor.

Oddly enough then for me, after over four years of trying to find an alternate factoring method with a concept I call surrogate factoring it all depended on this little thing that with

x^2 = y^2 + T - 2(k+6j)^2 - 3(k+6j)r

the j^2 will tend to dominate as you move around the correct value, which forces r to be negative to compensate.

That is just so amazing to me. How such a little thing is so important.

Without that, there'd be no clue about how to get close to k, and best you could loop through searching modulo p, which is what I worked at before, but the other crucial thing was realizing that

k^2 = (nT)(2)^{-1} mod p

was the REALLY important way to go as generalizing I used a variable I call α, but it turns out that with the generalization

z = (1+2α^2)x

and it's just easier to force z divisible by 3 than it is some of the other values that can be, like 19, or 73.

All easy math, and easy to play with thankfully. Something of a subtle result though that requires you just do this odd thing of looking at

2x = k + pr

along with z = x+k, and z^2 = y^2 + nT, and then it's easy, as long as you do all those things and can argue it out for months until it all comes together.

Wow. Cool. What a result.

As consider

2x = k + 3r

when

z^2 = y^2 + T

where T is the target to be factored, is odd and coprime to 3, and T mod 3 = 2, as then z must have 3 as a factor, so

z = x+k

gives

x^2 + 2xk + k^2 = y^2 + T

which is x^2 = y^2 + T - 2xk - k^2, and I can substitute out 2x, to get

x^2 = y^2 + T - 2k^2 - 3kr

and that's where a nifty thing pops in, as, you want r=0, but in general, r will be NEGATIVE if you start with the optimal k when r=0 and move about modulo 6, as that k will be even. That's because you'd have

x^2 = y^2 + T - 2(k+6j)^2 - 3(k+6j)r

and if you have positive k (no reason to use negative) and try to move with positive j, then r will be negative, and even if you move with negative j, the 36j^2 term will tend to dominate, forcing r to be negative to compensate.

So r = 0 should be near the value at which abs(T-2k^2) is a minimum.

Trouble is, if you continue the analysis you find that k at that point is the minimum that might work—remember k is positive—but the actual k MUST be within k/6 steps from that value.

But it gives you a sense of what is possible, just with p=3.

I generalized to p odd prime though, but found that it's still important to have z with 3 as a factor, but then you have as a crucial requirement:

k^2 = (nT)(2)^{-1} mod p

so you need a prime for which k exists, and then you find a maximal k modulo that prime, as the same argument above works, except now you'd have

2x = k + pr

and you have a solution within k/(2p) steps from the maximal k.

If T mod 3 = 2, then you'd use n=1, else you'd use n=5 or maybe 2, I'm still not sure, to force nT mod 3 = 2, as there is a crucial requirement that

z = 3x

so z has to have 3 as a factor.

Oddly enough then for me, after over four years of trying to find an alternate factoring method with a concept I call surrogate factoring it all depended on this little thing that with

x^2 = y^2 + T - 2(k+6j)^2 - 3(k+6j)r

the j^2 will tend to dominate as you move around the correct value, which forces r to be negative to compensate.

That is just so amazing to me. How such a little thing is so important.

Without that, there'd be no clue about how to get close to k, and best you could loop through searching modulo p, which is what I worked at before, but the other crucial thing was realizing that

k^2 = (nT)(2)^{-1} mod p

was the REALLY important way to go as generalizing I used a variable I call α, but it turns out that with the generalization

z = (1+2α^2)x

and it's just easier to force z divisible by 3 than it is some of the other values that can be, like 19, or 73.

All easy math, and easy to play with thankfully. Something of a subtle result though that requires you just do this odd thing of looking at

2x = k + pr

along with z = x+k, and z^2 = y^2 + nT, and then it's easy, as long as you do all those things and can argue it out for months until it all comes together.

Wow. Cool. What a result.

### Tuesday, February 19, 2008

## JSH: Goes to my worries about factoring

So now with the full surrogate factoring theory, results are coming fast and furious and I'll admit being very, very, very surprised that an RSA number might be factored by p=3 and a fairly simple technique.

Those looking over the argument may recognize that there is only one area where it's even maybe kind of looking like I didn't feel in the blanks which is with how you find k.

But just try it. Factor a few numbers and you'll get that weird, giddy out of this world feeling like maybe you stepped into the Twilight Zone.

Reading over posters ranting and raving in reply to me is kind of weird now. It's like there is something oddly wrong with them, but I can't quite put my finger on it.

The challenges to factor an RSA public key though, seem to be answerable now, and I'm mainly just absorbing the latest and the sense of profound oddity of it all.

You can factor an RSA public key, if that key is 2 modulo 3, and if with

z^2 = y^2 + public key

z is divisible by 3, and the math will just do it and kind of wink at you as if it wasn't even hard.

And you get k by finding k such that abs(public key - 2k^2 ) is a minimum and k is even, and you have two possibles k = 1 mod 3, or k = -1 mod 3.

Then x = k/2, and z = 3x, and you get y and factor the public key.

Just like that.

Yup, I had reason to worry about factoring. Wacky. Factoring a public key with p=3. Who would have thought the RSA system would crash so profoundly?

Here's another example: T = (101)(103) = 10403, so trying k=-1 mod 3 (as I already know that k = 1 mod 3 won't work):

k = 68 is the maximal k, such that abs (10403 - 2k^2) is a minimum.

x = k/3 = 34. z = x + k = 102. 102^2 - 10403 = 1. y = 1, so

Should be x = k/2. I'm feeling very stressed out at this point.

z-y = 101, z+y = 103

and that could just as easily been an RSA public key.

Still seems so weird though. So easy. All that work people did for all those years and the answer is so easy.

And it's trivial math, like I explained in a previous post about helper primes.

The primes were there to help all along.

The prime numbers were there to help all along.

They step in and they step out.

I really don't think that my research was ignored by accident or honest mistakes in considering it. I got the one paper published in SWJPAM and the damn journal editors pulled it under SOCIAL pressure from sci.math'ers. Newsgroup people influencing math editors.

And then the freaking journal died.

Mathematicians went on the run, that's all. Rather than accept that they had things wrong they thought they could just lie and rely in me not being believed.

Think about all those undergrads taught crap math deliberately when they could have been taught real mathematics.

Over five years of undergrads.

Deliberately taught wrong.

And I've contacted Ribet, and I've contacted Mazur, so who knows what Wiles knew. He did not find a proof of Fermat's Last Theorem.

His research fails with a simple logical fallacy.

How gone do people have to be when they can't be moved by the fate of the human race? When they can claim to be at the pinnacle of mathematics when they're teaching wrong information and blocking the correct?

What about our future?

So they didn't know how to factor.

Why is that a surprise? They didn't know much mathematics at all.

Those looking over the argument may recognize that there is only one area where it's even maybe kind of looking like I didn't feel in the blanks which is with how you find k.

But just try it. Factor a few numbers and you'll get that weird, giddy out of this world feeling like maybe you stepped into the Twilight Zone.

Reading over posters ranting and raving in reply to me is kind of weird now. It's like there is something oddly wrong with them, but I can't quite put my finger on it.

The challenges to factor an RSA public key though, seem to be answerable now, and I'm mainly just absorbing the latest and the sense of profound oddity of it all.

You can factor an RSA public key, if that key is 2 modulo 3, and if with

z^2 = y^2 + public key

z is divisible by 3, and the math will just do it and kind of wink at you as if it wasn't even hard.

And you get k by finding k such that abs(public key - 2k^2 ) is a minimum and k is even, and you have two possibles k = 1 mod 3, or k = -1 mod 3.

Then x = k/2, and z = 3x, and you get y and factor the public key.

Just like that.

Yup, I had reason to worry about factoring. Wacky. Factoring a public key with p=3. Who would have thought the RSA system would crash so profoundly?

Here's another example: T = (101)(103) = 10403, so trying k=-1 mod 3 (as I already know that k = 1 mod 3 won't work):

k = 68 is the maximal k, such that abs (10403 - 2k^2) is a minimum.

x = k/3 = 34. z = x + k = 102. 102^2 - 10403 = 1. y = 1, so

Should be x = k/2. I'm feeling very stressed out at this point.

z-y = 101, z+y = 103

and that could just as easily been an RSA public key.

Still seems so weird though. So easy. All that work people did for all those years and the answer is so easy.

And it's trivial math, like I explained in a previous post about helper primes.

The primes were there to help all along.

The prime numbers were there to help all along.

They step in and they step out.

I really don't think that my research was ignored by accident or honest mistakes in considering it. I got the one paper published in SWJPAM and the damn journal editors pulled it under SOCIAL pressure from sci.math'ers. Newsgroup people influencing math editors.

And then the freaking journal died.

Mathematicians went on the run, that's all. Rather than accept that they had things wrong they thought they could just lie and rely in me not being believed.

Think about all those undergrads taught crap math deliberately when they could have been taught real mathematics.

Over five years of undergrads.

Deliberately taught wrong.

And I've contacted Ribet, and I've contacted Mazur, so who knows what Wiles knew. He did not find a proof of Fermat's Last Theorem.

His research fails with a simple logical fallacy.

How gone do people have to be when they can't be moved by the fate of the human race? When they can claim to be at the pinnacle of mathematics when they're teaching wrong information and blocking the correct?

What about our future?

So they didn't know how to factor.

Why is that a surprise? They didn't know much mathematics at all.

## Surrogate factoring and helper primes

The real story is that I was finishing out the theory on surrogate factoring.

z^2 = y^2 mod T

I wondered a few years ago if there weren't another way where you could connect factorizations, and after years of research I've found that with

z^2 = y^2 + nT,

where n is some non-zero integer I can add a few more variables using

z = x+αk, so

(x+αk)2 = y^2 + nT

and if you have k and α, and if k = 2αx then you find

x^2 = y^2 + nT - (1 + α^2)k^2.

You may recall I talked a lot recently about factors mod p, where p is an odd prime, as now is where helper primes come in allowing you to solve for k modulo p:

k^2 = (α^2+1)^{-1}(nT) mod p.

So how did I introduce prime p? Actually with

2αx = k + pr_2

so the full equation is actually

x^2 = y^2 + nT - (1 + α^2)k^2 + kpr_2

but if you find k such that the absolute value of nT - (1 + α^2)k^2 is a minimum, then you minimize the absolute value of r_2 as well, and make it 0.

So the primes help you find the factorization and then vanish without a trace, which is why I call them helper primes.

To see one in operation, let T=119 and n=1, and p = 3.

Then

k^2 = (α^2+1)^{-1}(nT) mod p = (α^2+1)^{-1}(119) mod 3.

And α = 1 works giving k^2 = 1 mod 3, so I can use any integer k coprime to 3.

And finding k such that the absolute value of 119 - 2k^2 is a minimum gives k=8.

Then I have x = 4, just like that, and substituting

16 = y^2 + 119 - 128 = y^2 - 9

so y = 5, and

z = x + αk = 4 + 8 = 12, and z-y = 12-5 = 7, and z+y = 12+5 = 17.

Notice that p=3 just helped and then vanished without a trace.

And yes, it IS possible than an RSA public key could be factored by p=3.

However you can just as well get a trivial factorization, or find that you can't use 3, as nT mod 3 must equal 2. But then you can use p=5. Or p = 7.

Or any odd prime that you liked until you broke it as the math does not care.

It is unlikely that you would need a large prime for a composite of only two prime factors.

Surrogate factoring exploits the fact that every composite factorization is connected to an infinity of other factorizations, so you can use those factorizations to factor your target.

Mathematicians focused primarily on congruences of squares that made the target the modulus while I ranged beyond that exploring an idea.

Surrogate factoring was a concept that is now a fully fleshed out theory.

z^2 = y^2 mod T

I wondered a few years ago if there weren't another way where you could connect factorizations, and after years of research I've found that with

z^2 = y^2 + nT,

where n is some non-zero integer I can add a few more variables using

z = x+αk, so

(x+αk)2 = y^2 + nT

and if you have k and α, and if k = 2αx then you find

x^2 = y^2 + nT - (1 + α^2)k^2.

You may recall I talked a lot recently about factors mod p, where p is an odd prime, as now is where helper primes come in allowing you to solve for k modulo p:

k^2 = (α^2+1)^{-1}(nT) mod p.

So how did I introduce prime p? Actually with

2αx = k + pr_2

so the full equation is actually

x^2 = y^2 + nT - (1 + α^2)k^2 + kpr_2

but if you find k such that the absolute value of nT - (1 + α^2)k^2 is a minimum, then you minimize the absolute value of r_2 as well, and make it 0.

So the primes help you find the factorization and then vanish without a trace, which is why I call them helper primes.

To see one in operation, let T=119 and n=1, and p = 3.

Then

k^2 = (α^2+1)^{-1}(nT) mod p = (α^2+1)^{-1}(119) mod 3.

And α = 1 works giving k^2 = 1 mod 3, so I can use any integer k coprime to 3.

And finding k such that the absolute value of 119 - 2k^2 is a minimum gives k=8.

Then I have x = 4, just like that, and substituting

16 = y^2 + 119 - 128 = y^2 - 9

so y = 5, and

z = x + αk = 4 + 8 = 12, and z-y = 12-5 = 7, and z+y = 12+5 = 17.

Notice that p=3 just helped and then vanished without a trace.

And yes, it IS possible than an RSA public key could be factored by p=3.

However you can just as well get a trivial factorization, or find that you can't use 3, as nT mod 3 must equal 2. But then you can use p=5. Or p = 7.

Or any odd prime that you liked until you broke it as the math does not care.

It is unlikely that you would need a large prime for a composite of only two prime factors.

Surrogate factoring exploits the fact that every composite factorization is connected to an infinity of other factorizations, so you can use those factorizations to factor your target.

Mathematicians focused primarily on congruences of squares that made the target the modulus while I ranged beyond that exploring an idea.

Surrogate factoring was a concept that is now a fully fleshed out theory.

### Friday, February 15, 2008

## JSH: Frustrated.

Maybe I should say more after going on and on about an approach that I now accept was just useless for factoring, but I keep thinking about why I'm so desperate for something in the factoring area anyway, which is the blocking of my "pure math" research where math people don't follow their own rules.

I NEED a practical math result because one dead journal shows how locked down math society has it now.

Maybe we'll take each other down before all of this is over and I'll get my way of convincing the world that mathematicians routinely lie and your society will find a way to get me in return.

And it is a sad testimony to the true reality of modern academia.

It is a medieval system. And you end up in medieval crap with it, like what I call the Math Wars.

Some of you seem to think the Math Wars are just fun and games or just some silly "crackpot" mouthing off, but it is about me finding a way to do things like end tenure, reduce funding for academics and convince the world that objective measures, rather than just letting academics say which of their buddies supposedly did something great, are necessary.

So sit back. Think you have it all handled as I remain frustrated, and venting in futile anger at a feudal system of academia, because I need that practical mathematical result to break a broken system, but remember, it only takes one result for me to then go back and use every moment like this to emphasize to the public why it needs to do as much as necessary.

Our modern world exists today because discovery was cherished.

But parasites have turned things upside down for a few dollars and some empty accolades because they can't appreciate the value.

If humanity loses then it loses down the line, and the extinction of our species whenever it occurs as we probably won't manage to get off this planet, may trace back to a tragic shift, when major problem solving was lost, and pretend took over.

Call me crazy. But then nothing I do will work in the real world, right?

But then you won't find funding drying up, and you won't find an increasingly skeptical public demanding more than just your say-so, right?

Call me crazy, and if I am then the solutions I find to convince people that your society lies in the real world won't really be solutions, right?

But I see the end of the Math Wars putting most of you in other areas of work outside of mathematics. But my vision is against your will to stop me.

We'll see who wins down the line.

I NEED a practical math result because one dead journal shows how locked down math society has it now.

Maybe we'll take each other down before all of this is over and I'll get my way of convincing the world that mathematicians routinely lie and your society will find a way to get me in return.

And it is a sad testimony to the true reality of modern academia.

It is a medieval system. And you end up in medieval crap with it, like what I call the Math Wars.

Some of you seem to think the Math Wars are just fun and games or just some silly "crackpot" mouthing off, but it is about me finding a way to do things like end tenure, reduce funding for academics and convince the world that objective measures, rather than just letting academics say which of their buddies supposedly did something great, are necessary.

So sit back. Think you have it all handled as I remain frustrated, and venting in futile anger at a feudal system of academia, because I need that practical mathematical result to break a broken system, but remember, it only takes one result for me to then go back and use every moment like this to emphasize to the public why it needs to do as much as necessary.

Our modern world exists today because discovery was cherished.

But parasites have turned things upside down for a few dollars and some empty accolades because they can't appreciate the value.

If humanity loses then it loses down the line, and the extinction of our species whenever it occurs as we probably won't manage to get off this planet, may trace back to a tragic shift, when major problem solving was lost, and pretend took over.

Call me crazy. But then nothing I do will work in the real world, right?

But then you won't find funding drying up, and you won't find an increasingly skeptical public demanding more than just your say-so, right?

Call me crazy, and if I am then the solutions I find to convince people that your society lies in the real world won't really be solutions, right?

But I see the end of the Math Wars putting most of you in other areas of work outside of mathematics. But my vision is against your will to stop me.

We'll see who wins down the line.

## JSH: Enough venting, but funding is an issue

Ok, so enough venting out my frustrations with the math community. They're liars, so what? But funding for academia is increasingly a concern as I think, yup, that we're spending too much given the returns.

Yeah, I know, supposedly all this activity out there is going to lead to something big down the line and there are people doing fantastic research that is pushing our technology ever forward but I really feel that most of you are duds working the system.

And I think that about academics in general.

So the trendline that I'm pushing, for real, not just venting, is reducing funding and looking for survival of the fittest.

I don't buy the line that academics doing real research can't justify why the public should dole out money to pay their bills.

IF you can't explain why your research is worth the public dime, I think the public has a right to take it away.

It is our money.

The exceptions in my mind remain, materials science, medicine, biology, including anything to do with genetics, and, um, I think there was something else but I can't remember right now.

As for the rest, I want survival of the fittest and I want a lot more pressure on universities with big endowments—far, far, far more than you're starting to see now.

I want justifications across the board for monetary expenditures as I look to the world to weed out parasites: people who just are playing the game and not doing anything of value.

That effort is just beginning.

Yeah, I know, supposedly all this activity out there is going to lead to something big down the line and there are people doing fantastic research that is pushing our technology ever forward but I really feel that most of you are duds working the system.

And I think that about academics in general.

So the trendline that I'm pushing, for real, not just venting, is reducing funding and looking for survival of the fittest.

I don't buy the line that academics doing real research can't justify why the public should dole out money to pay their bills.

IF you can't explain why your research is worth the public dime, I think the public has a right to take it away.

It is our money.

The exceptions in my mind remain, materials science, medicine, biology, including anything to do with genetics, and, um, I think there was something else but I can't remember right now.

As for the rest, I want survival of the fittest and I want a lot more pressure on universities with big endowments—far, far, far more than you're starting to see now.

I want justifications across the board for monetary expenditures as I look to the world to weed out parasites: people who just are playing the game and not doing anything of value.

That effort is just beginning.

### Thursday, February 14, 2008

## JSH: What if no one believes you?

What do any of you have if no one believes you? Or better yet, if society doesn't?

I burn credibility because I'm right.

I don't need it, but in looking at my solutions people feel that I'm right so I can go out here and burn the belief in certainty itself.

Maybe it's all shades of gray, right?

What if NO one is right?

What if all the academics really are just saying stuff, that if not verifiable could just as well be something else?

What if you people do not matter?

Who listens to you now anyway?

I took from you what you didn't even know you could lose, and now you have no way of getting it back, without even accepting that it's gone.

End goal is simple: news people will not publish "pure math" results, at all.

That is the end goal.

I talk to a lot of people behind the scenes about politics, the economy, business as I cover a lot of territory with answers that work in the real world.

And I tell people that you people lie. That academics lie. That universities have endowments that are too big, and that people doing valuable research should be able to prove it, so we should slash funds and get survival of the fittest.

We must slash funding across the board and reduce expenditures at universities and colleges around the world is the message.

And it doesn't matter what you say, as I want you to disagree with people who bring arguments to you when you don't even accept who the source is.

And that is a continual process.

It never stops.

The drumbeat to the policy makers does not end.

And when I feel like it I come here and I just make a big mess.

You people broke your own rules thinking that ended it.

But the end of it will be when I cut your funding.

I burn credibility because I'm right.

I don't need it, but in looking at my solutions people feel that I'm right so I can go out here and burn the belief in certainty itself.

Maybe it's all shades of gray, right?

What if NO one is right?

What if all the academics really are just saying stuff, that if not verifiable could just as well be something else?

What if you people do not matter?

Who listens to you now anyway?

I took from you what you didn't even know you could lose, and now you have no way of getting it back, without even accepting that it's gone.

End goal is simple: news people will not publish "pure math" results, at all.

That is the end goal.

I talk to a lot of people behind the scenes about politics, the economy, business as I cover a lot of territory with answers that work in the real world.

And I tell people that you people lie. That academics lie. That universities have endowments that are too big, and that people doing valuable research should be able to prove it, so we should slash funds and get survival of the fittest.

We must slash funding across the board and reduce expenditures at universities and colleges around the world is the message.

And it doesn't matter what you say, as I want you to disagree with people who bring arguments to you when you don't even accept who the source is.

And that is a continual process.

It never stops.

The drumbeat to the policy makers does not end.

And when I feel like it I come here and I just make a big mess.

You people broke your own rules thinking that ended it.

But the end of it will be when I cut your funding.

## JSH: So it's not a solution

It's just depressing. The math people can't be beaten unless I solve the factoring problem because they lie about proofs so I need something they can't lie about, and that's it.

So I'm stuck. They'll win.

Yeah I did get published. In SWJPAM after nine months when I even told them before publication I was an amateur.

I despise mathematicians.

And never ever again tell me that publication matters as it doesn't if the "experts" just decide to ignore it, or even break it, like those sci.math'ers did, getting that journal to pull my paper after publication.

They are scum. They lie and they know it and there's no way to stop them.

NEVER ever again tell me that publication matters.

It doesn't.

Mathematicians are the scum of the earth. They lie and they know they lie and there's no way to stop them because they are beneath contempt.

They are beneath contempt.

Ranted a bit, then I went back to wondering why this latest idea wasn't working. And I figured it out.

So, um, all the previous about potential negative impact applies.

Looks like only I had that deep down gut feeling that two primes could be used in this way, so if the math people tried what I had before, they might have noticed it didn't work but didn't realize that they should puzzle out why as it SHOULD work.

So they just went back to whatever they were doing supposing I'd failed, I guess.

I got upset, got depressed, and then just went back to problem solving as that's what I do.

And I figured it out.

So I'm stuck. They'll win.

Yeah I did get published. In SWJPAM after nine months when I even told them before publication I was an amateur.

I despise mathematicians.

And never ever again tell me that publication matters as it doesn't if the "experts" just decide to ignore it, or even break it, like those sci.math'ers did, getting that journal to pull my paper after publication.

They are scum. They lie and they know it and there's no way to stop them.

NEVER ever again tell me that publication matters.

It doesn't.

Mathematicians are the scum of the earth. They lie and they know they lie and there's no way to stop them because they are beneath contempt.

They are beneath contempt.

Ranted a bit, then I went back to wondering why this latest idea wasn't working. And I figured it out.

So, um, all the previous about potential negative impact applies.

Looks like only I had that deep down gut feeling that two primes could be used in this way, so if the math people tried what I had before, they might have noticed it didn't work but didn't realize that they should puzzle out why as it SHOULD work.

So they just went back to whatever they were doing supposing I'd failed, I guess.

I got upset, got depressed, and then just went back to problem solving as that's what I do.

And I figured it out.

## JSH: Scary situation, getting scarier

So I solved the factoring problem by doing some simple things and it's an easy proof and it's easy to check to verify with some simple numbers to see that I have a solution that must work, but that was days ago.

How could mathematicians not report this major find?

Well let me tell you a story. Years ago I pioneered a technique in mathematical analysis which turns a lot of established ideas in mathematics upside down and even got a paper on it published in a peer reviewed mathematical journal.

I've talked about that many times before, but the rest of the story is that I didn't just give up when the now defunct journal SWJPAM went belly-up a few months after withdrawing my paper AFTER publication after pressure from the math community against it.

But rather than elaborate on what I faced I'll point out that out of the blue a math grad student from Cornell University sent me an email offering to help. He claimed to be interested in having me explain to him my ideas and that the upside to me could be support from someone at Cornell.

So I sent him a beginning argument of a few pages. He sent back questions which I dutifully answered, but I noticed he took longer and longer between question so that a simple math argument of mostly algebra was taking this grad student MONTHS to work through.

After one long pause in his email he talked about long walks in the early morning hours like around 3 a.m. or something and I knew he was nearly gone.

Coming to the final pieces of the argument—remember I sent him beginning stuff—he finally replied back that he needed to get another math text, and that was it.

I've had a mathematician go on an immediate sabbatical when a colleague tried to help me out by having him look over some of my research on prime numbers.

A six month sabbatical.

When he returned he claimed he had never been asked about it, but refused to look at it.

I had one math professor just tell me that an equation that I knew worked—as it counted prime numbers—could not work, and he refused to be dissuaded.

They snap.

Now the factoring problem is solved. It's an easy solution but people who thought they were brilliant are wrapped up with people who are just con artists and neither of them are doing the right thing.

You physics people need to wake up to what can happen to you as well as everybody else.

The math people have gone bye bye. There is a solution to the factoring problem and it is TRIVIAL.

Hey, guess what? You could lose your funding! Your entire university could find itself stopped in its tracks if mad hackers go wild on your systems!!!

DO SOMETHING you people. Or while you sit twiddling your thumbs civilization as we know it can go up in flames and you won't be doing research on advanced computer systems but maybe writing things out on whatever scraps of paper you can find between foraging for food and dodging wild dogs.

DO SOMETHING BEFORE IT IS TOO LATE.

THE MATH PEOPLE WILL NOT.

How could mathematicians not report this major find?

Well let me tell you a story. Years ago I pioneered a technique in mathematical analysis which turns a lot of established ideas in mathematics upside down and even got a paper on it published in a peer reviewed mathematical journal.

I've talked about that many times before, but the rest of the story is that I didn't just give up when the now defunct journal SWJPAM went belly-up a few months after withdrawing my paper AFTER publication after pressure from the math community against it.

But rather than elaborate on what I faced I'll point out that out of the blue a math grad student from Cornell University sent me an email offering to help. He claimed to be interested in having me explain to him my ideas and that the upside to me could be support from someone at Cornell.

So I sent him a beginning argument of a few pages. He sent back questions which I dutifully answered, but I noticed he took longer and longer between question so that a simple math argument of mostly algebra was taking this grad student MONTHS to work through.

After one long pause in his email he talked about long walks in the early morning hours like around 3 a.m. or something and I knew he was nearly gone.

Coming to the final pieces of the argument—remember I sent him beginning stuff—he finally replied back that he needed to get another math text, and that was it.

I've had a mathematician go on an immediate sabbatical when a colleague tried to help me out by having him look over some of my research on prime numbers.

A six month sabbatical.

When he returned he claimed he had never been asked about it, but refused to look at it.

I had one math professor just tell me that an equation that I knew worked—as it counted prime numbers—could not work, and he refused to be dissuaded.

They snap.

Now the factoring problem is solved. It's an easy solution but people who thought they were brilliant are wrapped up with people who are just con artists and neither of them are doing the right thing.

You physics people need to wake up to what can happen to you as well as everybody else.

The math people have gone bye bye. There is a solution to the factoring problem and it is TRIVIAL.

Hey, guess what? You could lose your funding! Your entire university could find itself stopped in its tracks if mad hackers go wild on your systems!!!

DO SOMETHING you people. Or while you sit twiddling your thumbs civilization as we know it can go up in flames and you won't be doing research on advanced computer systems but maybe writing things out on whatever scraps of paper you can find between foraging for food and dodging wild dogs.

DO SOMETHING BEFORE IT IS TOO LATE.

THE MATH PEOPLE WILL NOT.

## JSH: Simple matching, factoring versus math politics

Playing around with various approaches to the factoring problem I noticed that if I did something as simple as consider T = 9 mod 11 and T = 2 mod 13, I would find that the minimum positive number for T that would work would be 119, which is a number I like to use in my examples and it occurred to me that the primes were forcing something.

So I started thinking about what information prime numbers could give about factors as if the two primes were forcing T to be 119 or greater, then they were also forcing the factors to be certain values.

So I expanded out a factorization with primes:

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = (r_1 + k_1*p_1)

and

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

And I multiplied out and solved for k_1 and k_2 respectively and again pondered, what if you GUESSED using f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2, so you'd know the f's and the g's?

And I realized that then you could use

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

and

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)

and reduce to a solution for d_1.

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and then you also need d_2, so

d_2 = (f_2 - g_2)*p_2^{-1} mod p_1.

So suddenly I had it!!! Information from the intersection of the primes.

The two prime numbers were now telling me something about a key variable in the expanded factorization!!!

And now you can go back to

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

multiply out, and divide by p_2, using m_2 = (g_1*g_2/p_2), and you can get to

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

so now you just substitute modulo p_1 and compare what you get on the right side with k_2 mod p_1 as you know what k_2 is, since

k_2 = floor(T/p_2).

Now then, does this work?

Well, is there an answer for d_1 mod p_1 and d_2 mod p_2?

Of course, yes. If I have the correct residues for the f's and g's then will that answer be given by

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and

d_2 = (f_2 - g_2)*p_2^{-1} mod p_1?

The answer is, of course, yes.

Now perturb them. Shift f_1 or g_1 and will you change d_1 and d_2?

YES!!!

So then, this method will work to tell you when you have them correctly so the answer to the key question of factoring is available: what is f_1 mod p_1 and f_2 mod p_2?

As you answer that question prime by prime you can factor the target, as a minimum positive value for f_1 is forced, like T = 9 mod 11 and T = 2 mod 13 forced a minimum positive value for T.

Now that is easy math. Trivial algebra.

Hating mathematics is about hating truths that you don't like, and I know that feeling so I can understand why so many of you despise mathematics, even if you claim to be mathematicians.

You despise it because you do not control it.

That's why your society came up with "delicate proofs" and "logical contradictions" as you found a human solution to an inhuman discipline.

The math does not care. What's true is true even if you can't make a living in the field telling the truth.

So most of you learned to lie as otherwise, you'd have to make your living some other way, and if society let you, why not live the fantasy?

Why not just pretend? Why not act? Actors are heroes in this society right?

Like Melanie Griffith. Or Brad Pitt. Or Morgan Freeman. Or Claire Forlani.

Actors make big bucks, and get accolades so why not just act with mathematics too?

So if they could, why not you?

So I started thinking about what information prime numbers could give about factors as if the two primes were forcing T to be 119 or greater, then they were also forcing the factors to be certain values.

So I expanded out a factorization with primes:

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = (r_1 + k_1*p_1)

and

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

And I multiplied out and solved for k_1 and k_2 respectively and again pondered, what if you GUESSED using f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2, so you'd know the f's and the g's?

And I realized that then you could use

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

and

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)

and reduce to a solution for d_1.

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and then you also need d_2, so

d_2 = (f_2 - g_2)*p_2^{-1} mod p_1.

So suddenly I had it!!! Information from the intersection of the primes.

The two prime numbers were now telling me something about a key variable in the expanded factorization!!!

And now you can go back to

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

multiply out, and divide by p_2, using m_2 = (g_1*g_2/p_2), and you can get to

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

so now you just substitute modulo p_1 and compare what you get on the right side with k_2 mod p_1 as you know what k_2 is, since

k_2 = floor(T/p_2).

Now then, does this work?

Well, is there an answer for d_1 mod p_1 and d_2 mod p_2?

Of course, yes. If I have the correct residues for the f's and g's then will that answer be given by

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and

d_2 = (f_2 - g_2)*p_2^{-1} mod p_1?

The answer is, of course, yes.

Now perturb them. Shift f_1 or g_1 and will you change d_1 and d_2?

YES!!!

So then, this method will work to tell you when you have them correctly so the answer to the key question of factoring is available: what is f_1 mod p_1 and f_2 mod p_2?

As you answer that question prime by prime you can factor the target, as a minimum positive value for f_1 is forced, like T = 9 mod 11 and T = 2 mod 13 forced a minimum positive value for T.

Now that is easy math. Trivial algebra.

Hating mathematics is about hating truths that you don't like, and I know that feeling so I can understand why so many of you despise mathematics, even if you claim to be mathematicians.

You despise it because you do not control it.

That's why your society came up with "delicate proofs" and "logical contradictions" as you found a human solution to an inhuman discipline.

The math does not care. What's true is true even if you can't make a living in the field telling the truth.

So most of you learned to lie as otherwise, you'd have to make your living some other way, and if society let you, why not live the fantasy?

Why not just pretend? Why not act? Actors are heroes in this society right?

Like Melanie Griffith. Or Brad Pitt. Or Morgan Freeman. Or Claire Forlani.

Actors make big bucks, and get accolades so why not just act with mathematics too?

So if they could, why not you?

### Tuesday, February 12, 2008

## JSH: Problem solving techniques

I use modern problem solving techniques. Those techniques recognize failure as just part of the process and brainstorming is one of the most known where lots of failures are just expected.

But the modern math world is corrupted.

So posters use those failures to try and hide the successes, even when it's the factoring problem—or a proof of Fermat's Last Theorem.

There were Catholic priests who turned out to be pedophiles (and nuns). Enron collapsed dramatically. And "pure math" mathematicians lie.

The world goes on.

Now as to why they lie it's simple: math is hard.

There are too many people who are supposedly mathematicians doing valuable research in the world today.

It's just so hard to do real research in mathematics that there is no way all those people are.

There just isn't that much discovery possible for a species at our level.

So most of what they're doing is fake as you can make a living as a math professor and produce papers, and have a job where most people haven't a clue what you're doing, so they don't know it's fake.

But you have one problem: every once in a while these pesky discoverers come around who want to do REAL mathematics as if that stuff is valuable, and they have this annoying tendency to want to tell the truth about mathematical ideas!!!

So your professors came up with a system to stop them, which involves ignoring answers or insulting them a lot, like calling them insane.

Not a bad system, and I discovered how potent it is, but it has one fatal flaw: discoverers are problem solvers.

So a mathematical discoverer at a certain level would just consider their system another problem to solve and figure out a way to dismantle it.

It's a challenge. I like challenges. And I'm good at solving problems.

So I decided your group was just another challenge, another problem to solve as a measure of how good I am. Neat.

So they just gave me a challenge. That's all.

Oh yeah, they ARE fakes. From what I've seen, not much real mathematics is being done in "pure math" areas today.

Maybe in topology. I think topology is ok.

But the modern math world is corrupted.

So posters use those failures to try and hide the successes, even when it's the factoring problem—or a proof of Fermat's Last Theorem.

There were Catholic priests who turned out to be pedophiles (and nuns). Enron collapsed dramatically. And "pure math" mathematicians lie.

The world goes on.

Now as to why they lie it's simple: math is hard.

There are too many people who are supposedly mathematicians doing valuable research in the world today.

It's just so hard to do real research in mathematics that there is no way all those people are.

There just isn't that much discovery possible for a species at our level.

So most of what they're doing is fake as you can make a living as a math professor and produce papers, and have a job where most people haven't a clue what you're doing, so they don't know it's fake.

But you have one problem: every once in a while these pesky discoverers come around who want to do REAL mathematics as if that stuff is valuable, and they have this annoying tendency to want to tell the truth about mathematical ideas!!!

So your professors came up with a system to stop them, which involves ignoring answers or insulting them a lot, like calling them insane.

Not a bad system, and I discovered how potent it is, but it has one fatal flaw: discoverers are problem solvers.

So a mathematical discoverer at a certain level would just consider their system another problem to solve and figure out a way to dismantle it.

It's a challenge. I like challenges. And I'm good at solving problems.

So I decided your group was just another challenge, another problem to solve as a measure of how good I am. Neat.

So they just gave me a challenge. That's all.

Oh yeah, they ARE fakes. From what I've seen, not much real mathematics is being done in "pure math" areas today.

Maybe in topology. I think topology is ok.

## JSH: It's a hard life

People think that life is easy now when most of humanity is struggling out there, while a few people—percentage wise—are living large. So they think something has changed because they personally are desperate for attention versus eating, or having clean water.

But all that has changed is the illusion of a change has gotten

stronger.

The difference now is that our mistakes can lead to the extinction of the human species.

And that would kind of suck.

Problem solving is not just a way to get attention. Science is not about impressing people with how smart you are. And publish or perish is about the survival of our species, when it's right.

I can assure you that many of you are lost. You are lost souls who think the world is a giant piggy bank with endless funds and it doesn't matter if you lie, cheat and steal because SOMEONE will save the day down the line, or you just don't believe in much of anything so you think that nothing matters, except what you can take.

Except I can tell people exactly what you take and that you don't think anything matters except what you take.

The window is closing for us.

There is only so much time to get things together before we close the door on life on this planet which is what the small-minded people out there think can't happen, so they make it inevitable.

Yes, we can kill life on this planet, and in doing so, end our own as well.

But out of the tragedy that I think is rapidly closing, whether you can see it or not, or believe it or not, if it happens nothing you think can stop it, or even pause it, and your stupidity won't save a single living thing, maybe some life can survive, and with it, a soaring future can be realized.

Our sister planet is Venus. She is our twin. We are heading towards her fate.

It's time to get ready to go. Humanity will have to leave planet earth, and soon.

Whether you like it or not, or believe it or not.

Some of us will be going.

The rest of you will, well, you can figure it out.

But all that has changed is the illusion of a change has gotten

stronger.

The difference now is that our mistakes can lead to the extinction of the human species.

And that would kind of suck.

Problem solving is not just a way to get attention. Science is not about impressing people with how smart you are. And publish or perish is about the survival of our species, when it's right.

I can assure you that many of you are lost. You are lost souls who think the world is a giant piggy bank with endless funds and it doesn't matter if you lie, cheat and steal because SOMEONE will save the day down the line, or you just don't believe in much of anything so you think that nothing matters, except what you can take.

Except I can tell people exactly what you take and that you don't think anything matters except what you take.

The window is closing for us.

There is only so much time to get things together before we close the door on life on this planet which is what the small-minded people out there think can't happen, so they make it inevitable.

Yes, we can kill life on this planet, and in doing so, end our own as well.

But out of the tragedy that I think is rapidly closing, whether you can see it or not, or believe it or not, if it happens nothing you think can stop it, or even pause it, and your stupidity won't save a single living thing, maybe some life can survive, and with it, a soaring future can be realized.

Our sister planet is Venus. She is our twin. We are heading towards her fate.

It's time to get ready to go. Humanity will have to leave planet earth, and soon.

Whether you like it or not, or believe it or not.

Some of us will be going.

The rest of you will, well, you can figure it out.

### Monday, February 11, 2008

## JSH: Factoring IS stupid simple

Ok, sorry, as I hate it to some extent when a problem turns out to be harder to solve than I thought when some part of me must kind of know the answer but it takes a while for the rest of me to get it.

Here's the correct answer to the factoring problem where I just kind of diverged a bit before.

I was puzzling about the latest failed factoring idea wondering where I went wrong, as I really felt that there was information wrapped up in the intersection of the residues modulo T of two primes.

So I pondered some more.

Before too long I was writing out things along these lines:

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = (r_1 + k_1*p_1)

and

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

And I multiplied out and solved for k_1 and k_2 respectively and again pondered what if you GUESSED using f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2, so you'd know the f's and the g's, and I realized that then you could just solve for the c's by using

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

and

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)

and I realized you could solve for everything and reduce to a solution for d_1.

That's from before, but after that point, before, I went in the wrong direction as it is so OBVIOUS what you should do next, which is solve d_1 modulo p_1 (maybe I was sleepy when I first typed that last).

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and then you also need d_2, so

d_2 = (f_1 - g_2)*p_2^{-1} mod p_1

and now you can substitute modulo p_1 into, oh, forgot something:

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

multiply out, and divide by p_2, using m_2 = (g_1*g_2/p_2), and you can get to

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

so now you just substitute modulo p_1 and compare what you get on the right side with k_2 mod p_1 as you know what k_2 is, since

k_2 = floor(T/p_2).

If you guessed correctly then you will match with k_2's residue modulo p_1, but if you didn't, you shouldn't match unless this doesn't work either!!!

So if you don't match you try another possible and try until you match, and do that for a series of primes where the total is less than m, such that T/m! < 1, or you can get an exact number by multiplying primes together—assuming you start with the smallest and go up—until you exceed T, and counting how many you have.

That is the solution to the factoring problem.

It's stupid simple.

I just took a little time to figure out exactly how the damn thing worked.

But that's problem solving for you. Some part of me must have known the answer but the rest of me was stupid, until simple won.

[A reply to someone who asked James why doesn't he just guess p1 such that T/p1 is integer.]

Funny. Ok, yes, I admit it. I went on and on about having solved the factoring problem through an intersection of primes when I hadn't shown it.

So I had a strong feeling that there had to be a way to do it, and then got waylaid in figuring out exactly how, but this latest result is actually consistent with the original idea while what I had before was not.

Here you DO test, and the guess just gets you SOME information, so you need a series of primes.

The approach IS straightforward and it is stupid, simple, so get mad and upset about the problem solving process but that just shows you have no clue how it really works.

Mostly it's about hard work, lots of misses and being willing to keep beating on that hunch until it pays off, and later let the freaking historians re-write history and talk about what a genius you are.

It's a big mess until you're right.

During the process most of the time you feel like a freaking idiot.

[A reply to someone who said that the issue is to find an efficient algorithm.]

If the approach holds i.e. if the values for d_1 mod p_1 and d_2 mod p_1 are provisional values that work only when you guess correctly, then this approach DOES lead to an efficient algorithm.

It turns out that it is well-known that if you have f_1 mod p_1, and f_1 mod p_2, … f_1 mod p_n, where n is a sufficient number of primes then you have f_1 explicitly.

The problem though has been, how do you find f_1 modulo successive primes?

I contemplated this issue and hypothesized that when you have two primes you have some kind of intersection that will give the answer, and I went looking for that intersection.

My first approaches went awry as I tried to actually solve for d_1 exactly, but thinking about why those approaches didn't work, I looked at the equations again and saw:

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and I had everything I needed where BOTH primes gave input, so I had my intersection.

So this approach IS a valuable one as long as the hypothesis holds true and the value of d_1 modulo p_1 found above is invalid unless you've guessed f_1 and g_1 correctly, as those are residues, where

f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2

and are NOT the full solutions. Maybe I could have picked other variable letters.

In any event, the point is an intersection between two primes with a guess at residues and checking to see if the guess is right.

If you can do that then factoring is trivial as you need less primes than m, where T/m! < 1.

So you have factorial working for you here, and that is a big over-estimate for m.

If this approach holds water then factoring an RSA public key of any size possible on modern desktop computers would be trivially done in minutes if not seconds.

The factoring problem is solved by using the intersection of prime numbers, in an elegant, precise, and remarkably short solution.

Here's the correct answer to the factoring problem where I just kind of diverged a bit before.

I was puzzling about the latest failed factoring idea wondering where I went wrong, as I really felt that there was information wrapped up in the intersection of the residues modulo T of two primes.

So I pondered some more.

Before too long I was writing out things along these lines:

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = (r_1 + k_1*p_1)

and

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

And I multiplied out and solved for k_1 and k_2 respectively and again pondered what if you GUESSED using f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2, so you'd know the f's and the g's, and I realized that then you could just solve for the c's by using

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

and

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)

and I realized you could solve for everything and reduce to a solution for d_1.

That's from before, but after that point, before, I went in the wrong direction as it is so OBVIOUS what you should do next, which is solve d_1 modulo p_1 (maybe I was sleepy when I first typed that last).

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and then you also need d_2, so

d_2 = (f_1 - g_2)*p_2^{-1} mod p_1

and now you can substitute modulo p_1 into, oh, forgot something:

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

multiply out, and divide by p_2, using m_2 = (g_1*g_2/p_2), and you can get to

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

so now you just substitute modulo p_1 and compare what you get on the right side with k_2 mod p_1 as you know what k_2 is, since

k_2 = floor(T/p_2).

If you guessed correctly then you will match with k_2's residue modulo p_1, but if you didn't, you shouldn't match unless this doesn't work either!!!

So if you don't match you try another possible and try until you match, and do that for a series of primes where the total is less than m, such that T/m! < 1, or you can get an exact number by multiplying primes together—assuming you start with the smallest and go up—until you exceed T, and counting how many you have.

That is the solution to the factoring problem.

It's stupid simple.

I just took a little time to figure out exactly how the damn thing worked.

But that's problem solving for you. Some part of me must have known the answer but the rest of me was stupid, until simple won.

[A reply to someone who asked James why doesn't he just guess p1 such that T/p1 is integer.]

Funny. Ok, yes, I admit it. I went on and on about having solved the factoring problem through an intersection of primes when I hadn't shown it.

So I had a strong feeling that there had to be a way to do it, and then got waylaid in figuring out exactly how, but this latest result is actually consistent with the original idea while what I had before was not.

Here you DO test, and the guess just gets you SOME information, so you need a series of primes.

The approach IS straightforward and it is stupid, simple, so get mad and upset about the problem solving process but that just shows you have no clue how it really works.

Mostly it's about hard work, lots of misses and being willing to keep beating on that hunch until it pays off, and later let the freaking historians re-write history and talk about what a genius you are.

It's a big mess until you're right.

During the process most of the time you feel like a freaking idiot.

[A reply to someone who said that the issue is to find an efficient algorithm.]

If the approach holds i.e. if the values for d_1 mod p_1 and d_2 mod p_1 are provisional values that work only when you guess correctly, then this approach DOES lead to an efficient algorithm.

It turns out that it is well-known that if you have f_1 mod p_1, and f_1 mod p_2, … f_1 mod p_n, where n is a sufficient number of primes then you have f_1 explicitly.

The problem though has been, how do you find f_1 modulo successive primes?

I contemplated this issue and hypothesized that when you have two primes you have some kind of intersection that will give the answer, and I went looking for that intersection.

My first approaches went awry as I tried to actually solve for d_1 exactly, but thinking about why those approaches didn't work, I looked at the equations again and saw:

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and I had everything I needed where BOTH primes gave input, so I had my intersection.

So this approach IS a valuable one as long as the hypothesis holds true and the value of d_1 modulo p_1 found above is invalid unless you've guessed f_1 and g_1 correctly, as those are residues, where

f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2

and are NOT the full solutions. Maybe I could have picked other variable letters.

In any event, the point is an intersection between two primes with a guess at residues and checking to see if the guess is right.

If you can do that then factoring is trivial as you need less primes than m, where T/m! < 1.

So you have factorial working for you here, and that is a big over-estimate for m.

If this approach holds water then factoring an RSA public key of any size possible on modern desktop computers would be trivially done in minutes if not seconds.

The factoring problem is solved by using the intersection of prime numbers, in an elegant, precise, and remarkably short solution.

## JSH: Factoring problem solution, update

I stumbled across a remarkably simple solution to the factoring problem, which exists because of what is called the floor() function. That function just means to drop any fractions or decimals, so like floor(3.1415) = 3.

It is crucial to the solution to the factoring problem.

Here is the full solution.

It suffices to determine variables to fulfill the factorizations:

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = r_1 + k_1*p_1

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = r_2 + k_2*p_2

where T is the target to be factored and p_1 and p_2 are primes to be picked, as this method works because you're using primes in this way which is why you need so many variables.

Note that f_1, f_2, g_1 and g_2 are residues where

f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2.

So the r's and k's are easily calculated and the only remaining variables are c_1, c_2, d_1 and d_2, and you guess at values for the f's and g's. So guessing is crucial in this method.

And it can be shown that solving for the factors reduces to finding integer solutions to a family of 4 equations and 4 unknowns, which are

k_1 = c_1*f_2 + c_2*f_1 + c_1*c_2*p_1 + m_1

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)

where m_1 = floor(f_1*f_2/p_1) and m_2 = floor(g_1*g_2/p_2).

However, if the primes lack enough residues for all the solutions of T, then an intermediate solution is forced as all of the equations will not then be interdependent, and then you can solve for the c_1 in the first equation and d_1 in the second to get

c_1 = (k_1 - m_1 - c_2*f_1)/(f_2 + c_2*p_1)

and

d_1 = (k_2 - m_2 - d_2*g_1)/(g_2 + d_2*p_2)

and divide through by the denominator to get to a number that is factored to find an integer c_2, and an integer d_2, where that cannot be done with the original set of equations as the numerator is T itself, so that is equivalent to factoring T.

But here, crucially, the m's break you from directly getting T, so that

k_1 - m_1 - c_2*f_1 does not equal T

and

k_2 - m_2 - d_2*g_1 does not equal T

(curious readers can substitute the m's out wrongly with m_1 = f_1*f_2/p_1 and m_2 = g_1*g_2/p_2 and see what happens—you get T back).

So m_1 and m_2 are crucial to the solution as floor() is a discrete function.

If you have guessed the right f's and g's then your integer solutions for the c's and d's will give you a factorization of T, otherwise

(f_1 + c_1*p_1)(f_2 + c_2*p_1)

and

(g_1 + d_1*p_2)(g_2 + d_2*p_2)

will equal some other number.

If you have selected the correct f's and g's then you will get integer solutions, otherwise you will not, so if you do not then you shift to another set, so there are

(p_1 - 1)(p_2 - 1)

MAXIMUM total checks without regard to the size of T.

If you have fewer prime residues available than factors of T, then you will not be able to solve for the c's and d's exactly but must use the approach mentioned above, but if you do have enough residues you will have 4 independent equations and can just solve for the variables, and will get integers when you have the correct residues.

It is a fantastic solution where the floor() function does all the heavy lifting, creating a logical situation that provides for a trivial solution to the factoring problem.

If the solution is ignored then civilization as we know it may end.

And it can do so within a few days, my analysis indicates.

Which would be the end of humanity's halcyon period.

Many of you might simply die of starvation, if you're lucky.

[A reply to someone who asked James why should anyone care about the value of floor (3.1416).

Because I found a solution to the factoring problem, but the academic world is corrupted so I couldn't present it in a way designed to have the least negative impact.

Which means that the solution can be exploited and end civilization as we know it if mathematicians continue to do what I think they'll do.

Didn't you read the post The Art of War? Didn't get it?

If these math people are as powerful as I think they are, then no way would they just leave it to chance that some genius could come in and wreck their system, so they had to believe they were safe.

But they know I found a proof of Fermat's Last Theorem so I maybe could figure out the factoring problem, right?

So why am I still here?

They must have something up their sleeves so I declared all these solutions to the problem that turned out to be bogus and then got lucky and found the right answer.

If it's correct, then, for instance, the entire Internet could be on its knees in a few days and you wouldn't have to worry about what I or anyone else posts as you wouldn't SEE any posts.

Yup, for the rest of you, no more posting for anyone. Get it? Concerned yet? Willing to help?

(I think that might have more of an impression than the possibility of starvation. God knows some of you have to post.)

If I'm right, the world as you know it is going to change.

Just because of some math wars the entire Internet could be in flames in a few days, if I'm right.

Read that Art of War story.

[James replies to his own first post, up to the point where he wrote “m_1 = floor(f_1*f_2/p_1) and m_2 = floor(g_1*g_2/p_2)”.]

Well I started out correctly but from there went down the wrong path.

But the intuition that I was following was that the intersection of primes gives information about factoring, which was such a strong gut feeling that when I realized I'd screwed up, I went back over to see where I might have gone wrong, and, well, found the trivial solution.

So I backtracked a bit and then found the correct path.

Turns out you next need to solve for d_1 modulo p_1:

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and then you also need d_2, so

d_2 = (f_1 - g_2)*p_2^{-1} mod p_1

and now you can substitute modulo p_1 into, oh, forgot something:

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

multiply out, and divide by p_2, using m_2 = (g_1*g_2/p_2), and you can get to

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

so now you just substitute modulo p_1 and compare what you get on the right side with k_2 mod p_1 as you know what k_2 is, since

k_2 = floor(T/p_2).

If you guessed correctly then you will match with k_2's residue modulo p_1, but if you didn't, you shouldn't match unless this doesn't work either!!!

So if you don't match you try another possible and try until you match, and do that for a series of primes where the total is less than m, such that T/m! < 1, or you can get an exact number by multiplying primes together—assuming you start with the smallest and go up—until you exceed T, and counting how many you have.

That is the solution to the factoring problem.

It is a key in the lock technique. When you have the right residues of factors modulo each prime then

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and

d_2 = (f_1 - g_2)*p_2^{-1} mod p_1

are the right keys in the lock so that you get

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2.

For those wondering if maybe it's wrong, imagine you have the WRONG f's and g's, then the d's should be different, right?

So when they're right…

Easy solution but a lot of inertia I'm sure because of so much invested in thinking factoring is hard.

Of course, if too much time is taken then, well, I've harped enough on the potential negative consequences.

I just have to hope that there are adults around.

[A reply to someone who wrote speed is of the essence.]

I'm using the factoring problem.

If as I fear math society IS corrupt then it possibly knows that potentially I could solve the factoring problem to prove that, so crooks within that society must feel they have a backup.

But what?

My guess is that they have protocols in place with the Bush administration and with agreements between nations where such a solution would be sealed away, along with the discoverer.

But how can they seal away what they don't know exists?

And that's where you came in, you and other posters on the newsgroups.

You helped provide the distance—the gap—between when they might know and when they wouldn't.

So everything now is about how effective you've been.

You see, I don't want you to believe me now.

I want the opposite.

That gives the solution time to propagate and force the situation, and take away the final solution from unethical governments, like the Bush administration.

Same plan in place for those willing to help: work in concert, with a display that takes away any notion that governments can seal this away and hide it, along with me.

My survival depends on your execution.

Work well.

It is crucial to the solution to the factoring problem.

Here is the full solution.

It suffices to determine variables to fulfill the factorizations:

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = r_1 + k_1*p_1

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = r_2 + k_2*p_2

where T is the target to be factored and p_1 and p_2 are primes to be picked, as this method works because you're using primes in this way which is why you need so many variables.

Note that f_1, f_2, g_1 and g_2 are residues where

f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2.

So the r's and k's are easily calculated and the only remaining variables are c_1, c_2, d_1 and d_2, and you guess at values for the f's and g's. So guessing is crucial in this method.

And it can be shown that solving for the factors reduces to finding integer solutions to a family of 4 equations and 4 unknowns, which are

k_1 = c_1*f_2 + c_2*f_1 + c_1*c_2*p_1 + m_1

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)

where m_1 = floor(f_1*f_2/p_1) and m_2 = floor(g_1*g_2/p_2).

However, if the primes lack enough residues for all the solutions of T, then an intermediate solution is forced as all of the equations will not then be interdependent, and then you can solve for the c_1 in the first equation and d_1 in the second to get

c_1 = (k_1 - m_1 - c_2*f_1)/(f_2 + c_2*p_1)

and

d_1 = (k_2 - m_2 - d_2*g_1)/(g_2 + d_2*p_2)

and divide through by the denominator to get to a number that is factored to find an integer c_2, and an integer d_2, where that cannot be done with the original set of equations as the numerator is T itself, so that is equivalent to factoring T.

But here, crucially, the m's break you from directly getting T, so that

k_1 - m_1 - c_2*f_1 does not equal T

and

k_2 - m_2 - d_2*g_1 does not equal T

(curious readers can substitute the m's out wrongly with m_1 = f_1*f_2/p_1 and m_2 = g_1*g_2/p_2 and see what happens—you get T back).

So m_1 and m_2 are crucial to the solution as floor() is a discrete function.

If you have guessed the right f's and g's then your integer solutions for the c's and d's will give you a factorization of T, otherwise

(f_1 + c_1*p_1)(f_2 + c_2*p_1)

and

(g_1 + d_1*p_2)(g_2 + d_2*p_2)

will equal some other number.

If you have selected the correct f's and g's then you will get integer solutions, otherwise you will not, so if you do not then you shift to another set, so there are

(p_1 - 1)(p_2 - 1)

MAXIMUM total checks without regard to the size of T.

If you have fewer prime residues available than factors of T, then you will not be able to solve for the c's and d's exactly but must use the approach mentioned above, but if you do have enough residues you will have 4 independent equations and can just solve for the variables, and will get integers when you have the correct residues.

It is a fantastic solution where the floor() function does all the heavy lifting, creating a logical situation that provides for a trivial solution to the factoring problem.

If the solution is ignored then civilization as we know it may end.

And it can do so within a few days, my analysis indicates.

Which would be the end of humanity's halcyon period.

Many of you might simply die of starvation, if you're lucky.

[A reply to someone who asked James why should anyone care about the value of floor (3.1416).

Because I found a solution to the factoring problem, but the academic world is corrupted so I couldn't present it in a way designed to have the least negative impact.

Which means that the solution can be exploited and end civilization as we know it if mathematicians continue to do what I think they'll do.

Didn't you read the post The Art of War? Didn't get it?

If these math people are as powerful as I think they are, then no way would they just leave it to chance that some genius could come in and wreck their system, so they had to believe they were safe.

But they know I found a proof of Fermat's Last Theorem so I maybe could figure out the factoring problem, right?

So why am I still here?

They must have something up their sleeves so I declared all these solutions to the problem that turned out to be bogus and then got lucky and found the right answer.

If it's correct, then, for instance, the entire Internet could be on its knees in a few days and you wouldn't have to worry about what I or anyone else posts as you wouldn't SEE any posts.

Yup, for the rest of you, no more posting for anyone. Get it? Concerned yet? Willing to help?

(I think that might have more of an impression than the possibility of starvation. God knows some of you have to post.)

If I'm right, the world as you know it is going to change.

Just because of some math wars the entire Internet could be in flames in a few days, if I'm right.

Read that Art of War story.

[James replies to his own first post, up to the point where he wrote “m_1 = floor(f_1*f_2/p_1) and m_2 = floor(g_1*g_2/p_2)”.]

Well I started out correctly but from there went down the wrong path.

But the intuition that I was following was that the intersection of primes gives information about factoring, which was such a strong gut feeling that when I realized I'd screwed up, I went back over to see where I might have gone wrong, and, well, found the trivial solution.

So I backtracked a bit and then found the correct path.

Turns out you next need to solve for d_1 modulo p_1:

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and then you also need d_2, so

d_2 = (f_1 - g_2)*p_2^{-1} mod p_1

and now you can substitute modulo p_1 into, oh, forgot something:

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = (r_2 + k_2*p_2)

multiply out, and divide by p_2, using m_2 = (g_1*g_2/p_2), and you can get to

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

so now you just substitute modulo p_1 and compare what you get on the right side with k_2 mod p_1 as you know what k_2 is, since

k_2 = floor(T/p_2).

If you guessed correctly then you will match with k_2's residue modulo p_1, but if you didn't, you shouldn't match unless this doesn't work either!!!

So if you don't match you try another possible and try until you match, and do that for a series of primes where the total is less than m, such that T/m! < 1, or you can get an exact number by multiplying primes together—assuming you start with the smallest and go up—until you exceed T, and counting how many you have.

That is the solution to the factoring problem.

It is a key in the lock technique. When you have the right residues of factors modulo each prime then

d_1 = (f_1 - g_1)*p_2^{-1} mod p_1

and

d_2 = (f_1 - g_2)*p_2^{-1} mod p_1

are the right keys in the lock so that you get

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2.

For those wondering if maybe it's wrong, imagine you have the WRONG f's and g's, then the d's should be different, right?

So when they're right…

Easy solution but a lot of inertia I'm sure because of so much invested in thinking factoring is hard.

Of course, if too much time is taken then, well, I've harped enough on the potential negative consequences.

I just have to hope that there are adults around.

[A reply to someone who wrote speed is of the essence.]

I'm using the factoring problem.

If as I fear math society IS corrupt then it possibly knows that potentially I could solve the factoring problem to prove that, so crooks within that society must feel they have a backup.

But what?

My guess is that they have protocols in place with the Bush administration and with agreements between nations where such a solution would be sealed away, along with the discoverer.

But how can they seal away what they don't know exists?

And that's where you came in, you and other posters on the newsgroups.

You helped provide the distance—the gap—between when they might know and when they wouldn't.

So everything now is about how effective you've been.

You see, I don't want you to believe me now.

I want the opposite.

That gives the solution time to propagate and force the situation, and take away the final solution from unethical governments, like the Bush administration.

Same plan in place for those willing to help: work in concert, with a display that takes away any notion that governments can seal this away and hide it, along with me.

My survival depends on your execution.

Work well.

## JSH: Factoring problem solution, latest objections

Some posters have STILL been attacking the simple solution to the factoring problem so I will answer their claims and first point out a crucial step that I caught one of them doing which was removing m_1 and m_2.

You'll notice in what follows that m_1 = floor(f_1*f_2/p_1) and m_2 = floor(g_1*g_2/p_2) where all the variables will be explained. What's important here is that the floor() function creates an integer requirement, and is key to solving the factoring problem.

Without it, there is no solution.

So a poster sneakily taking out m_1 and m_2 is removing the very basis for the solution.

With that said there IS a situation when you can not find specific solutions which I need to address, so it's worth addressing that as well and I'll do so below.

The full system again is

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = r_1 + k_1*p_1

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = r_2 + k_2*p_2

set T to your target, and pick two primes p_1 and p_2.

Now f_1, f_2, g_1 and g_2 are residues where

f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2.

And it can be shown that solving for the factors reduces to finding integer solutions to a family of 4 equations and 4 unknowns, which are

c_1, c_2, d_1 and d_2:

k_1 = c_1*f_2 + c_2*f_1 + c_1*c_2*p_1 + m_1

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)

where m_1 = floor(f_1*f_2/p_1) and m_2 = floor(g_1*g_2/p_2).

However, if the primes lack enough residues for all the solutions of T, then the math has no choice but to kind of loop on itself, and not allow you to solve for the c's or d's, BUT you can still solve in that case:

c_1 = (k_1 - m_1 - c_2*f_1)/(f_2 + c_2*p_1)

and

d_1 = (k_2 - m_2 - d_2*g_1)/(g_2 + d_2*p_2)

c_1 = (k_1 - m_1 - c_2*f_1)/(f_2 + c_2*p_1)

and

d_1 = (k_2 - m_2 - d_2*g_1)/(g_2 + d_2*p_2)

Those are just incredible equations, as they give you something you

can't have without the floor() function as otherwise the m's are

fractions.

Stupid simple is what the answer to the factoring problem is.

Stupid simple.

where you can factor the numerators in each case to find integers that will work, which is an approach that cannot work, you'll notice with the original equations as you are then just factoring T itself!

Here it works because

m_1 = floor(f_1*f_2/p_1)

and

m_2 = floor(g_1*g_2/p_2)

though if the f's and g's are wrong when you substitute back in before, you won't get T.

So m_1 and m_2 are crucial to the solution as floor() is a discrete function.

If you have selected the correct f's and g's then you will get integer solutions, otherwise you will not, so then you'd shift to another set, so there are

(p_1 - 1)(p_2 - 1)

MAXIMUM total checks without regard to the size of T.

Modern mathematicians unfortunately lie. Their system collapses if they are caught so they CANNOT celebrate a fantastically simple proof as I'm telling them that I'll inform the world that they lie all the time.

So it's a fascinating situation. I'm curious how long the world will let them lie about the factoring problem since they can collapse civilization with the lie.

Seems a few days already, which makes you wonder how much rich people really value their billions.

Maybe they don't really care if they end up being poor, soon.

What continues to amaze me though are the students.

Getting taught crap ideas from people who really are kind of dumb would upset me.

My guess is that it's about not wanting to accept having wasted so much of your lives with junk ideas, so you take in more junk.

It's like after being told you were eating crap for caviar you stuff yourself with more out of denial.

They did it on purpose.

I just want you to know that they had to know they were wasting your time, your life, and your mind, and they did so because they are parasitic.

Just con artists masquerading as mathematicians.

Nothing more.

[A reply to someone who told James that it was time for him starting to delete posts.]

Let's see how confident you are tomorrow.

The math is in the post.

The m's would be fractions without the floor() function.

Your objections all centered on removing the floor() function.

Sigh. If I'm wrong, then so what? It's just another mistake of mine.

But if I'm right, then the destabilization of society is just around the corner.

And then it won't matter what dreams you used to have as the civilization necessary to realize them, will no longer exist.

You'll notice in what follows that m_1 = floor(f_1*f_2/p_1) and m_2 = floor(g_1*g_2/p_2) where all the variables will be explained. What's important here is that the floor() function creates an integer requirement, and is key to solving the factoring problem.

Without it, there is no solution.

So a poster sneakily taking out m_1 and m_2 is removing the very basis for the solution.

With that said there IS a situation when you can not find specific solutions which I need to address, so it's worth addressing that as well and I'll do so below.

The full system again is

(f_1 + c_1*p_1)(f_2 + c_2*p_1) = T = r_1 + k_1*p_1

(g_1 + d_1*p_2)(g_2 + d_2*p_2) = T = r_2 + k_2*p_2

set T to your target, and pick two primes p_1 and p_2.

Now f_1, f_2, g_1 and g_2 are residues where

f_1*f_2 = T mod p_1 and g_1*g_2 = T mod p_2.

And it can be shown that solving for the factors reduces to finding integer solutions to a family of 4 equations and 4 unknowns, which are

c_1, c_2, d_1 and d_2:

k_1 = c_1*f_2 + c_2*f_1 + c_1*c_2*p_1 + m_1

k_2 = d_1*g_2 + d_2*g_1 + d_1*d_2*p_2 + m_2

(f_1 + c_1*p_1) = (g_1 + d_1*p_2)

(f_2 + c_2*p_1) = (g_2 + d_2*p_2)

where m_1 = floor(f_1*f_2/p_1) and m_2 = floor(g_1*g_2/p_2).

However, if the primes lack enough residues for all the solutions of T, then the math has no choice but to kind of loop on itself, and not allow you to solve for the c's or d's, BUT you can still solve in that case:

c_1 = (k_1 - m_1 - c_2*f_1)/(f_2 + c_2*p_1)

and

d_1 = (k_2 - m_2 - d_2*g_1)/(g_2 + d_2*p_2)

c_1 = (k_1 - m_1 - c_2*f_1)/(f_2 + c_2*p_1)

and

d_1 = (k_2 - m_2 - d_2*g_1)/(g_2 + d_2*p_2)

Those are just incredible equations, as they give you something you

can't have without the floor() function as otherwise the m's are

fractions.

Stupid simple is what the answer to the factoring problem is.

Stupid simple.

where you can factor the numerators in each case to find integers that will work, which is an approach that cannot work, you'll notice with the original equations as you are then just factoring T itself!

Here it works because

m_1 = floor(f_1*f_2/p_1)

and

m_2 = floor(g_1*g_2/p_2)

though if the f's and g's are wrong when you substitute back in before, you won't get T.

So m_1 and m_2 are crucial to the solution as floor() is a discrete function.

If you have selected the correct f's and g's then you will get integer solutions, otherwise you will not, so then you'd shift to another set, so there are

(p_1 - 1)(p_2 - 1)

MAXIMUM total checks without regard to the size of T.

Modern mathematicians unfortunately lie. Their system collapses if they are caught so they CANNOT celebrate a fantastically simple proof as I'm telling them that I'll inform the world that they lie all the time.

So it's a fascinating situation. I'm curious how long the world will let them lie about the factoring problem since they can collapse civilization with the lie.

Seems a few days already, which makes you wonder how much rich people really value their billions.

Maybe they don't really care if they end up being poor, soon.

What continues to amaze me though are the students.

Getting taught crap ideas from people who really are kind of dumb would upset me.

My guess is that it's about not wanting to accept having wasted so much of your lives with junk ideas, so you take in more junk.

It's like after being told you were eating crap for caviar you stuff yourself with more out of denial.

They did it on purpose.

I just want you to know that they had to know they were wasting your time, your life, and your mind, and they did so because they are parasitic.

Just con artists masquerading as mathematicians.

Nothing more.

[A reply to someone who told James that it was time for him starting to delete posts.]

Let's see how confident you are tomorrow.

The math is in the post.

The m's would be fractions without the floor() function.

Your objections all centered on removing the floor() function.

Sigh. If I'm wrong, then so what? It's just another mistake of mine.

But if I'm right, then the destabilization of society is just around the corner.

And then it won't matter what dreams you used to have as the civilization necessary to realize them, will no longer exist.

### Sunday, February 10, 2008

## JSH: Art of War

I am a fan of the book THE ART OF WAR, and there is a great story in it about this great general who wanted to conquer this heavily fortified city so he encamped near it and prepared to attack, but he had no intentions of going through with it at that time.

Still as his army approached the city had no choice but to prepare so it closed its gates and its citizens rushed to their defensive positions.

At the last moment the general had his armies wheel away from attack, return to their camp and bed down.

He did this routinely for months.

The same drill each time, his troops would assemble for the assault, charge the city, the city would close its gates on go on the defensive, and then the general would wheel away.

So guess what happened?

The city grew complacent, and used to the drills, so one day, when the general came charging, they didn't even bother to close the gates and no one went to defensive positions as they thought it was just another drill.

But this time the general completed the assault and conquered the city.

Great story.

Still as his army approached the city had no choice but to prepare so it closed its gates and its citizens rushed to their defensive positions.

At the last moment the general had his armies wheel away from attack, return to their camp and bed down.

He did this routinely for months.

The same drill each time, his troops would assemble for the assault, charge the city, the city would close its gates on go on the defensive, and then the general would wheel away.

So guess what happened?

The city grew complacent, and used to the drills, so one day, when the general came charging, they didn't even bother to close the gates and no one went to defensive positions as they thought it was just another drill.

But this time the general completed the assault and conquered the city.

Great story.

## JSH: Sorry for ranting and raving

You'd think I'd just be happy with the realization that I DID solve the factoring problem, but I felt a lot of rage. I HAVE been right all along, and it IS true that academics have worked to block my research for years now.

And solving the factoring problem just scares me as well, as who knows how things will play out now.

But I think the realization that there are academics in this world who not only do not do real research but they deliberately work to block major discoveries to HIDE that they do not do real research just infuriated me.

How many of you are fakes?

How much "scientific research" are you doing that you know is crap, where you also work together to attack scientists doing legitimate research?

I think the problem is extremely widespread.

My case is a dramatic example but again I'm reminded of Dr. Halton Arp, a distinguished scientist who was an assistant to Hubble himself, who has the distinction of being both a major figure in his field—and supposedly a crackpot.

I don't agree with a lot of what he says, but I don't call him crazy, and I am flabbergasted at the major reason his colleagues do.

It seems to be all about cosmologists wishing to ignore strong evidence that their theories about red-shift are oversimplistic.

So they can claim that quasars and galaxies are further away than they really are and that we know more about the universe than we really do.

They squashed Dr. Arp's funding in the US and he had to flee to Germany.

The parasitic academics are a scourge on humanity.

They have no morals. They work to get money for bogus research and flawed research ideas and fight legitimate research because it endangers their cash flow.

So now we have a simple solution to the factoring problem and I'm afraid the same type academics in the math field will try to ignore it or hide it.

But this time that can mean a direct impact on every single one of you, so there is no just turning a blind eye hoping it's for the best, or thinking there is nothing you can do as if you do nothing then you may find it hard to eat in the coming months. You and your families.

Yup, you can help crash civilization as we know it, which is what parasitic organisms do: they destroy their hosts.

That these are human parasites does not end their impact but may make it worse and yes, you may not be able to eat, literally, in the coming months if they are not handled here.

So I'm back to ranting and raving a bit but it's such an impossible situation!!!

Mindless and immoral human beings who can't be bothered to care about humanity or its future lie mindlessly to make a few buck and to stop them civilization itself has to be endangered?

The work of countless people around the world who trusted society could be blown away in days?

Entire countries could bite the dust? Because some academics lie for a living?

When you understand the enormity of the situation I think you will think I'm being amazingly calm.

"Publish or perish" takes on an entirely new meaning now.

And solving the factoring problem just scares me as well, as who knows how things will play out now.

But I think the realization that there are academics in this world who not only do not do real research but they deliberately work to block major discoveries to HIDE that they do not do real research just infuriated me.

How many of you are fakes?

How much "scientific research" are you doing that you know is crap, where you also work together to attack scientists doing legitimate research?

I think the problem is extremely widespread.

My case is a dramatic example but again I'm reminded of Dr. Halton Arp, a distinguished scientist who was an assistant to Hubble himself, who has the distinction of being both a major figure in his field—and supposedly a crackpot.

I don't agree with a lot of what he says, but I don't call him crazy, and I am flabbergasted at the major reason his colleagues do.

It seems to be all about cosmologists wishing to ignore strong evidence that their theories about red-shift are oversimplistic.

So they can claim that quasars and galaxies are further away than they really are and that we know more about the universe than we really do.

They squashed Dr. Arp's funding in the US and he had to flee to Germany.

The parasitic academics are a scourge on humanity.

They have no morals. They work to get money for bogus research and flawed research ideas and fight legitimate research because it endangers their cash flow.

So now we have a simple solution to the factoring problem and I'm afraid the same type academics in the math field will try to ignore it or hide it.

But this time that can mean a direct impact on every single one of you, so there is no just turning a blind eye hoping it's for the best, or thinking there is nothing you can do as if you do nothing then you may find it hard to eat in the coming months. You and your families.

Yup, you can help crash civilization as we know it, which is what parasitic organisms do: they destroy their hosts.

That these are human parasites does not end their impact but may make it worse and yes, you may not be able to eat, literally, in the coming months if they are not handled here.

So I'm back to ranting and raving a bit but it's such an impossible situation!!!

Mindless and immoral human beings who can't be bothered to care about humanity or its future lie mindlessly to make a few buck and to stop them civilization itself has to be endangered?

The work of countless people around the world who trusted society could be blown away in days?

Entire countries could bite the dust? Because some academics lie for a living?

When you understand the enormity of the situation I think you will think I'm being amazingly calm.

"Publish or perish" takes on an entirely new meaning now.