## Wow, consider my latest--twin primes probability

With my story and my research it is easy to get perspective on just what has to be happening by considering any number of areas, but I'll give you one new one as over the weekend I thought about twin primes, and had a basic simple idea:

If x is prime, then if you loop through all the primes up to sqrt(x+2), and find that none of them divide x+2, then x+2 must be prime, or to put it another way, if

x+2 = 0 mod p

for each prime p up to sqrt(x+2) is NOT true, then x+2 is prime.

Turns out the probability that x+2 is prime relative to a given prime p, is easy as it's just

(p-2)/(p-1)

and you msy be wondering where I get that, when it's just 1 - 1/(p-1) as p-1 is the count of non-zero residues modulo p, like for 5, 1, 2, 3 and 4 are the residues modulo 5. So you take the odds that you get a residue that would mean x+2 is divisible by p, and just subtract that from 1 to get the odds that it will NOT be divisible by p.

And you just do that for each prime up to the sqrt(x+2), and multiply them together to get a probability that if x is prime, x+2 is prime, or, the probability given that x is prime that you have twin primes.

See:
http://mymath.blogspot.com/2006/07/twin-primes-probability_30.html

Now that is so easy you'd think it'd have been part of the mathematical literature a long time ago, but it looks like, scarily, mathematicians just got close, but never quite figured it out, as see

http://mathworld.wolfram.com/TwinPrimesConstant.html

where you can see (p-1)/(p-2) in some of the formulas they show, but I haven't seen the simple explanation for why it's there, and it gets worse.

So if x is prime the probability that x+2 is prime is given by

prob = ((p_j - 2)/(p_j - 1))*…*(1/2)

where j is the number of primes up to sqrt(x+2), and p_j is the jth prime.

And if you read my post you'll see I even found a way to relate this to Goldbach's conjecture, where I've just kept going with this REALLY simple idea, as why just consider 2? Why not consider an arbitrary even prime gap g?

Next thing you know, Goldbach's is right in front of you.

But why is ANY of this new??!!!

And can it be ignored? I hope not, but consider all the research I have at this point.

Like, why would they ignore any of my research, like my short proof of Fermat's Last Theorem?

## Questions of controversy

If you look over what I claim to have discovered and know much about mathematics, the first natural reaction if this story is new to you, is disbelief: how could any of those claims be true without math society recognizing them?

The simplest answer I have is, politics.

Regardless, why should anyone pay attention to someone outside of a discipline where that person claims to have major discoveries, shouldn't they just follow the rules and procedures for getting their research acknowledged? Isn't it a bad sign for such a person to be out on the web with big claims versus going to the academic institutions or journals?

But you see, I did follow the rules, even had a paper published in a now defunct math journal, and here's a site mirror:

http://www.emis.de/journals/SWJPAM/

The paper was published but then withdrawn by the editors when some Usenet people from the newsgroup sci.math sent emails claiming it was wrong:

http://www.emis.de/journals/SWJPAM/vol2-03.html

That journal managed one more edition and then died.

No news headlines. Nothing in the papers. But the story is that a supposed crackpot had a major paper published in a peer reviewed, established mathematical journal, there was furor on some math newsgroup, where some people from that group sent some emails and managed to get the paper yanked, but the aftermath was that the math journal only managed one more edition before dying.

And you probably never heard of any of this until now unless you're part of math society.

So then, what can I do if math people don't follow their own rules?

There is a dead math journal to show you how big the politics in this situation are.

Notice too that I'm being given few options. I have talked to mathematicians at universities both by email and in person. I have had a paper published as I mentioned, and yes, I did try to get it published in another math journal, and even had help—to no avail.

The real story here is that I have few options, and this is one of them. So that's why I am on the web in this way.

What else can I do?

### Saturday, July 29, 2006

Here's an overview of research that I want to focus on at this point in time. Most of it is on my blog mymath.blogspot.com as this group is meant to be a discussion area for number theory related to what is on the blog, so you can talk about cryptology, basic number theory, algebraic number theory, or any of a variety of subjects near, like computer programming related to number theory, etc. and I hope to do only minimal moderation if necessary, and objective criticisms are appreciated!

I have given a definition of mathematical proof:

http://mymath.blogspot.com/2005/07/definition-of-mathematical-proof.html

Figured out the key properties that define rings that are like the ring of integers:

http://mymath.blogspot.com/2005/03/object-ring.html

Found my own prime counting function, which unlike any other known relies on summing a partial difference equation, which is also why it finds primes on its own, unlike any other known:

http://mymath.blogspot.com/2005/06/counting-primes.html

Fighting mathematicians who have done their best to ignore my research I wrote the first prime counting function article for the Wikipedia, where my latest version is now found in the history of the current page:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&old...

There readers can see my prime counting function in its fully mathematicized "pure" form, and see how it is a summation, so they can make the leap to understanding how it relates to a partial differential equation and an integration.

I had a paper published in a formally peer reviewed mathematical journal—and then the editors withdrew it after sci.math pressure against it:

http://www.emis.de/journals/SWJPAM/vol2-03.html

Link is to a site mirror as the electronic journal DIED a few months later.

That paper covered some pioneering research advancing modular algebra or the algebra of congruences, extending on the work started by Gauss:

http://mymath.blogspot.com/2005/07/tautological-spaces-factoring.html

Which is a line of attack I used to find a short proof of Fermat's Last Theorem:

http://mymath.blogspot.com/2006/03/proof-of-fermats-last-theorem.html

But I've even considered problems in logic and set theory, handling supposed contradictions:

http://mymath.blogspot.com/2005/06/three-valued-logic.html

and

http://mymath.blogspot.com/2005/05/logical-formedness-axioms.html

and

http://mymath.blogspot.com/2005/06/3-logic-more-basics.html

Even some of my minor research is significant, as I talked about a simple way to find primes using quadratic residues:

http://mymath.blogspot.com/2006/04/method-for-quickly-finding-primes....

The only explanation given the breadth of my research, and dramatic events like a math journal imploding after publishing then retracting a paper of mine is that it is so huge that mathematicians who are living in a political society today—where their word is more important than their research—are fighting a war to deny acceptance of any of it.

If any piece of my research is acknowledged as important from my definition of mathematical proof to my ideas about finding primes then they have to fear that the world will realize what they are doing, so the math wars as I call them are political ones.

It is a fight of group power against mathematical truth.

## JSH: Iteration over

Ok, so that's it for this iteration. I'm going on indefinite hiatus now while I consider some things.

I'll also get to the boring and tedious business of deleting posts out of Google, where I need to do a more complete job this time.

THIS iteration did have its moments. Fun here and there, lots of the usual drama, and I learned a lot as usual.

That is all for now.

## JSH: Life IS fair

The reality is that the Universe follows rules.

By the rules, you people can't just be handled without giving you a chance.

Damn rules.

But luckily, time is almost up.

And the result so far is not a surprise.

It's just a matter of handling the paperwork, you might say.

You got to insult me, and I get to hit back.

I know you all, wherever you are. I've known you for quite some time.

And I have no mercy.

## JSH: My challenge

The challenge to me was never to destroy any of you, or to break you.

It's not like that's hard.

The challenge to me is not to crush this world.

It's not like that's hard.

The challenge to me is to find the good within so much that I see as wrong.

The challenge to me was always to find within my fears the understanding that I was always fighting myself.

There is not a lot that I can't do in this situation. None of you are hidden. None of you are anonymous.

I have potentially the full resources of the civilized world at my fingertips. The full power of the United States, and Europe, China and Russia among others to find any of you, wherever you may be, anywhere in the world.

The challenge to me is to bring you to the table to accept truth as the highest ideal.

Or, if you will not, to make certain that when there are consequences, no one truly doubts that they are fair.

After all, I am not above you, I am here with you, right here, in the mix, along with everyone else.

I can't just move like a god, destroy what I will, make what I will, without dealing with the consequences myself.

I have more patience than you can understand. So it's not about time.

If necessary, I can wait, wait for this generation to die, and try again, with the next one, or the one after that, as I have all the time I need.

## No options with math society

I don't know if any of you get it yet but the problem here that I'm having with math society is that if they want you out, you have no options.

No options.

Send a paper to get it published, even if you get lucky, like I got one through, you can have the paper yanked and the freaking math journal die, and it not matter.

It seems to me that many of you are naive about the kind of power the math society has.

And given that power, like people everywhere, they got corrupted.

So how do you know anything they tell you is true?

Why do they have to tell the truth?

There's no motivation. All they have to say is stuff that advances their careers in a perfect position, with perfect power, and no where else for anyone to go.

The world created a situation where people learned that no one really cared, so it's not even so much of negatives about mathematicians, as they're victims in a sense as well, of a world that lost sight of the importance of the mathematical field.

Some of you may think you know so many things when in reality you know what some career academics told you, in a situation where they can put things up against evidence that is talked about within the discipline, but shut-down by the majority to hold a position that they know the public likes or tolerates that is better for their careers.

So you can research Halton Arp if you want to delude yourself about how this all works, as if it's about me. It's not about me. It's about the system.

It's a simple thing—give people the power to lie and advance their careers with no fear of accountability and it will happen.

The world corrupted the mathematical field. It bears the responsibility.

[A reply to someone who suggested that James should publish his papers on the web.]

My work is on the web. I've put it all on my blog.

But hey, this is Usenet, so it's a perfect place to whine. I have the right to whine. I am joyfully whining.

Seriously though, one of the first things I learned is that it doesn't matter about all this connectivity and putting things out there as it can just be ignored.

You could have the cure for cancer and it could be on the web—and ignored.

The real world is that you have very few options in modern society to get people's attention when they don't want to give it, no matter what you have, and it's just not true that people really can pick out the wheat from the chaff.

They can't.

Reality is that people go with the crowd—whatever they think their crowd is.

And who knows what the truth is?

Best you can hope for is to die in your sleep.

Most of you will never even come close to the truth. You will never have much of a clue about anything real about reality itself.

And that is the truth.

But you will believe otherwise—against all evidence.

THAT is the human condition.

[A reply to someone who said that the problem with James is that he is an idiot.]

Social forces are powerful because without society, you will die.

I challenge your society, in your mind, so to you, I must be an idiot who does not get it.

When you know that without that society, you will die.

It's not really a maybe, as I feel confident that you are not someone who could survive without the support of society, so some people believe that because of their dependency, the majority is always right.

But the majority gets things wrong.

And without people willing to keep pushing against things that are wrong, the entire system eventually fails.

Notice that if I am right, then the proof is in the mathematical arguments that I have.

Greater attention would not make those arguments look better if they fail.

Limited attention allows correct arguments to be ignored despite being right.

The world has always been turned by individuals who have to do what most people think of as impossible.

So history has been determined by those people who have to push against the majority for the greater good, and ask people, to consider the truth as something more than just what people think, as more importantly, it's what a person can prove.

The truth is important because it is the truth, and a hallmark of the truth is that it can stand against opposition that is about the needs of the moment.

## SF: Explicit solution

Here's an explicit solution without the congruences showing how surrogate factoring can work for those of you who lack familiarity or confidence in congruence relationships.

Let

x^2 - y^2 = a*T

where x and y are to naturals to be determined, 'a' is some unknown integer and T is the target to be factored.

Now let

S = 2*x*k + b*T

where S and k are integers that will be chosen and 'b' is some unknown integer.

So adding y^2 to both sides with the first gives

x^2 = y^2 + a*T, and adding the second equation in gives

x^2 + 2*x*k = y^2 + S + (a-b)*T

so I can complete the square with

x^2 + 2*x*k + k^2 = y^2 + S + k^2 + (a-b)*T

so I have with some simplification and a focus on y:

y^2 = (x+k)^2 - S - k^2 + (a-b)*T

so

y = sqrt( (x+k)^2 - S - k^2 + (a-b)*T)

and I only have that a-b not equal 0, so I can burn a degree of freedome and now let

a - b = 1

and solve for x and y.

I think the explicit solution is necessary for those who are uncomfortable with congruences, as the situation now is beyond bizarre.

Oh yeah, it's now also clear why Tim Peters couldn't get this to always work before, as my original approach is like using

a-b = 0

here, but with slightly different equations and can also be made to work, by use of T itself, which locks the equations to your target composite.

Easy math people. No way if you look it over you can miss it, or not understand how big it should be, as I've found a way to get equal quadratic residues modulo a target composite T, which involves factoring some number other than T which I call the surrogate.

Easy math—potentially huge consequences.

The ball is now in your court.

It occurs to me that some of you may not know how to proceed from that equatio to solve for x and y, so here's how.

If you have S and k, like S=1, k=1, and use, let's say a-b=1 still so you have

y^2 = (x+k)^2 - 1 - 1 - T = (x+k)^2 - 2 - T

then solving for x and y is just a matter of factoring T+2.

I like to show that using factors f_1 and f_2, where

f_1 * f_2 = 4*(T+2), so

x+k = f_1 + f_2

and

y = f_1 - f_2

and you can see trivially that it all balances out.

So how might this method not work?

I'm puzzling over that, and it seems to me that there is nothing forcing 'a' and 'b' to be integers, while a-b is forced to be an integer, so maybe they can divide out T in both cases, which is the only mathematical way this technique could fail besides producing a trivial factorization, as otherwise it will factor T.

I like simple equations as they leave little room for error or confusion about how they work to hide.

Still it's just basic research at this point. I, still, have yet to factor with these ideas, as I work out the theory.

I'm a theory guy. I leave experimentation for the experimentalists.

Now then, why would 'a' and 'b' consistently block out a factorization by dividing off T?

[A reply to someone who said that James had other reasons for not wanting to do experiments.]

Look over the equations, there is only one way for the approach not to work, which is if 'a' and 'b' are fractions that divide off T, despite a-b being chosen to be an integer.

As an interesting sidepoint, there are 7 variables, and 3 equations, where T is the target composite, so you choose it, of course, and you choose S and k, which takes up 6 degrees of freedom, leaving the final one to be taken by looking for integer solutions to the square root, handling all degrees of freedom.

The approach expressed explicitly can be considered very easily from multiple angles, so there is that thing I love—simplicity.

Simple ideas remove the ability of people to cherry-pick just on the difficulty of anyone else understanding the ideas, and in this case, with factoring, they help make my other point that mathematicians routinely break their own rules.

So you can't get mathematicians to show interest in anything that they don't like, no matter what its mathematical value because they're like spoiled children completely used to using arbitrary decisions without regard to real mathematical value, and one of their arbitrary positions is keeping out people they label "crank", "crackpot", or "loons".

They have no true love of their discipline and no true interest in knowledge for its own sake, but care only about what suits their personal needs, where you can just look over my posting here, with a simple factoring idea, and consider their rejection of it.

And they're clearly not very bright as if these ideas DO have value then a lot of people in the world are going to be mad as hornets when they realize that what I said above is true, and mathematicians are not only weird in ways that most people knew about, but they don't actually care about their own field, or the impact of important research on others, as if they're not in the real world with the rest of us, but in
their own little self-created world.

## SF: Residues and factoring, simpler

Here's a simpler and more reliable version of my latest factoring idea, with T the target composite to be factored, start with the following congruences:

x^2 - y^2 = 0 mod T

S = 2*x*k mod T

The rest is trivially easy, as then you have

x^2 = y^2 mod T, and adding the second equation in gives

x^2 + 2*x*k = y^2 + S mod T

so I can complete the square with

x^2 + 2*x*k + k^2 = y^2 + S + k^2 mod T

and here's where I go differently than before as I focus on y to get

y^2 = (x+k)^2 - S - k^2 mod T

and now you can factor to solve for x and y, but here it's a little tricky, as they are meant to be residues modulo T, so you solve for x+k by picking some S and k, and some n so that you have the explicit

y = sqrt( (x+k)^2 - S - k^2 + n*T) mod T

where I stuck the mod T on the end to remind to take the residue modulo T, for y, and also you have to do the same internally in the calculation of x, which is done by factoring

S+k^2 - n*T

where since you can pick n, it probably would make sense to pick n=1.

This approach solves the problems with my earlier one focusing on x, where I was enthralled with the modular inverse and you'd pick S and x_res, where x_res = x mod T.

Once you've solved for x and y, you just plug back into the first congruence, so you'd check x+y and x-y for factors in common with T.

And that is the solid approach, which I don't like as much as the other route, but at least it doesn't have the problems of the other route in terms of sometimes not being modulo T.

## Factoring, basic research versus politics

For years I have been doing basic research on factoring, looking for a solution to the factoring problem, with a lot of failures and SPECTACULAR failures along the way. To me that's just the reality of basic research that you fail more than you succeed, but for others that is a tool to control the discussion and push other people in various directions.

However that political behavior is running into the reality of basic research as an evolving process with unpredictable outcomes, where a long run of failure can end with success, as I now clearly have a new factoring method. I'll recap the current research with the initial parts being a repeat of what has gone before as the research builds forward:

The factoring problem can be easily approached using simple algebra.

x^2 - y^2 = S - 2*x*k

where all are integers, as notice then you trivially have

x^2 + 2*x*k + k^2 = y^2 + S + k^2

so

x+k = sqrt(y^2 + S + k^2)

and finding y is just a matter of factoring (S+k^2)/4.

Now with just the explicit equation you end up with nothing but trivialities, but turning to congruences, you can now simply let

x^2 - y^2 = 0 mod T

which—this is important—now forces

S - 2*x_res*k = 0 mod T

where I put in x_res to emphasize that now it's congruences, so there is loose connectivity and an explicit value of x is not needed—just a residue.

But now I can just solve for k, assuming 2, S and x are coprime to T:

k = S*(2*x_res)^{-1} mod T

where (2*x_res)^{-1} is the modular inverse of (2*x_res) mod T.

That the modular inverse makes an appearance is critical, but more importantly I now have a way to find all the variables!!!

That can be done by simply picking a residue for x_res and then picking S, like x_res = 1, and S =1, to get k.

However, it can be shown that you will not get a solution for your target composite T, unless there exists a number Q such that

Q^2 + k^2 = (x_res^2 - S) mod T

which is the latest crucial result, without which, someone might stumble around trying different values and failing, think the approach was useless.

But that's why an open mind in basic research is important, and why politics should be left to other areas instead of mathematics and the sciences.

The problem I think today is that the current mathematical field is dominated by politicians masquerading as mathematicians, to the detriment of real research.

## When reasonable adults do nothing

What's so frustrating about my story is the lack of ANY options that work, as, for instance I had a math paper published!!! All it took was for some sci.math people to send some emails and get it yanked over night. When the journal had my paper for over nine months. And I spent years figuring out that mathematics.

The later death of the journal just makes the story bizarre and here's a link to the main site mirror:

http://www.emis.de/journals/SWJPAM/

That mirror site is important as, as far as I know, it is the last one, a and there you can read a bit about the now dead journal, and see how many other site mirrors there were.

How can that happen in our modern age?

It's easy for some of you to rationalize I think figuring that if I were a distinguished academic in the field, who wasn't going around talking about other academics being freaking liars, things would be different, but then there's Dr. Halton Arp in the astronomy field:

http://www.haltonarp.com/

He is distinguished in the field, he's actually dominant in the field—Google "Arp galaxies".

Now when I read news stories about academics declaring this or that in astronomy, I just don't believe them. I use to be very skeptical but I've gone to simply dismissing them outright.

The problem I think is that most adults just don't care.

So extreme stories can abound where one majority group is totally out there in terms of proof against its position that it ignores, while horrendous labeling is allowed and condoned, so when you speak out in your own defense, you're a "crackpot", "crank", or "loon" among other names.

I don't know how many times Usenet people have confidently diagnosed me as mentally ill.

The important point here is that there is no way with these people. They don't follow even their own rules, dismissing publication as if it were nothing.

Think about that—there is no way with these people.

They have given no route for others with outside opinions, even when you have done what reasonable adults should see as necessary, like getting publication. And no one is policing them, no one is holding them accountable, so why should they tell you the truth?

What makes you think you actually know much of anything that is true about our universe?

Years from now people like you may be a joke taught to students about how easily groups can become deluded about their own knowledge when so much evidence contrary to their beliefs was out there, but they went with a group of people who didn't even follow basic social rules?

How many people do you call crackpot on a daily basis?

How many people do you happily diagnose as mentally ill in your daily life when they disagree with you?

## Mathematicians routinely lie

I put this post up as a simple warning that mathematicians routinely lie about mathematics.

Some of you may think that impossible because of all the mathematics that you know is correct and works in the physics field, but there are lots of mathematical ideas in the "pure math" domain which I suggest to you are completely bogus, but mathematicians when faced with proofs of that, keep using them.

And they keep trying to bleed them over into the sciences, as well as their attituded and behaviors, as how else do you explain string theory?

Such a charge is difficult to convince people on, so I suggest you just ask yourself, what if?

What if mathematicians DO routinely lie about mathematics, how would you know?

Supposedly publication in a peer reviewed mathematical journal is the standard that separates the legitimate researchers from the "crackpots" who make all kinds of outlandish claims, which reasonable adults can assume are false when the experts don't back them up.

But I had a paper published in a peer reviewed mathematical journal.

Here's a link to a mirror site for the journal:

http://www.emis.de/journals/SWJPAM/vol2-03.html

There it says "Withdrawn" about my paper, but I didn't withdraw it, the editors did.—after someone posted on the sci.math newsgroup about the publication, so some sci.math'ers mounted an email campaign against the paper. They convinced the editors to abruptly yank it, and the journal managed one more edition before it keeled over and quietly died, after almost a decade of existence.

Here's the main mirror site with a list of what used to be the other site mirrors to give you some perspective on the journal's place before:

http://www.emis.de/journals/SWJPAM/

This story is several years old, and people seem to miss the crucial problem that if publication in a math journal is such a sketchy thing, and someone like myself is given no options by a community which has no qualms about questioning your mental health or tossing names at you like "crank", "crackpot", and "loon", how do you know anything they say is true?

How do you?

What makes you think that anything the mathematical community says about mathematics is actually true?

Remember, most of the mathematics used in physics that has been proven to work over time was known before the 20th century, while there are some new things that appear to work well, like group theory. But what about the rest?

How do you know that people who can so easily crush a paper publication, don't routinely lie?

I'm telling you that they do.

Dig into the story and find out why that paper was so important.

## Math world breaks own rules, questions

Supposedly publication in a peer reviewed mathematical journal is the standard that separates the legitimate researchers from the "crackpots" who make all kinds of outlandish claims, which reasonable adults can assume are false when the experts don't back them up.

But I had a paper published in a peer reviewed mathematical journal.

When someone posted that information on the newsgroup sci.math, there was an instant furor on the newsgroup.

Some of the posters went from maligning me and the journal—castigating the editors—to planning an assault on my paper with emails claiming it false.

The next day I got an email from the chief editor claiming publication had been a mistake.

So what can you do with a society that does not follow even its own rules?

You may wonder what details are there to this story I'm not telling that show that the withdrawal was correct.

More facts though, the journal had my paper for over nine months. I informed them early on that I was an amateur mathematician. They never sent me notice of any errors that they'd found. I've never had anyone find anything other than minor errors in the paper—to this day.

The chief editor yanked my paper overnight—clearly not enough time for a thorough check of all the facts, indicating he went with emotion.

Here's a link to a mirror site for the journal as after that debacle they managed one more edition before quietly shutting down:

http://www.emis.de/journals/SWJPAM/vol2-03.html

There it says "Withdrawn" about my paper, but I didn't withdraw it, the editors did.

There were about 10 mirror sites for the journal originally, but all others went away, and the original journal link at its home university no longer works.

I received an email from Mathematical Reviews (Never heard ot them? Google it.) a bit after the mess, as they were seeking author information to list me as a published author of a math paper, and I had to explain this situation and called them up, and talked to someone who had never heard of anything like it.

I did argue a lot of the ideas out on Usenet before writing a paper, as I naively used to think that talking out ideas was a good way to clear out crappy ones with the possibility that you could get pick up from experts who might help you write a paper, and afterwards I've found myself talking out ideas because it works for me in figuring them out.

The problem though with Usenet is that people can track you off Usenet, and come after you in other areas, like with what happened with my paper, and at this point, I don't see a solution.

It has been years since my paper was yanked.

So then, what do you do with a society that does not follow its own rules?

How can any of you truly know that I'm wrong in this situation and the math people—people not following their own rules—are right?

Yes, they call me names, like "crackpot", "crank", and "loon" among others.

And here I am on Usenet still, where I fear few will believe me, and even fewer will care.

But how do you know these people are telling you the truth about anything mathematical when they so casually break their own rules?

In retaliating against me and my paper, the sci.math newsgroup showed a weakness within the journal process and how EASILY a mob can take control over that process, and censor a paper.

That should have been news, but it wasn't, which is another troubling aspect of this story.

If I could get enough attention to the details of the paper, then people might see that it is correct, and should have been published, but math society has so much domination in this area that it simply can ignore competing views, and people like me are totally sidelined with little to do but grouse in what public spaces they can.

And math people stalk me in these spaces trying to intimidate me into silence, even telling me to stop posting—ever with the words "crank" or "crackpot" tossed about, or claims that I am mentally ill.

If you believe math people, posting when other people tell you to stop, is proof of mental illness. If you believe math people, daring to come up with your own mathematical ideas and hoping against hope that they are correct is a sign of mental illness.

And God help you if you admit failing repeatedly in your attempts to find a valid idea, as they'll attack you for that as well.

The only thing that would make these people happy is my total and complete silence.

## JSH: Truth is the highest ideal

You people have kept my interest for one reason and one reason only:

I need to understand how you lie.

Truth is the highest ideal.

I think most people want to be part of something bigger than themselves to feel like there is a great purpose which makes everything worthwhile.

But YOU people. You people seem to want nothing of reality at all.

So you ignore mathematical proof, and spit on logic.

You HATE when you should look for knowledge.

You insult, when you should ask, what if?

What is inside of you? What demons drive you? What snakes inhabit your souls?

How can you be?

I study you and wonder, and it seems like as much as I learn, there's more to learn.

## JSH: My world

Some of you seem to labor under the mistaken belief that you're doing something by replying to me saying some nonsense or other.

But I look out and see a world on fire.

You can deny it but every year brings more evidence that your world is dying and shredding and soon enough the people who will survive are the people smart enough to see the world as it is.

Plan for retirement. Have your savings. Behave as if the world is some fantasy.

And each year as global warming advances, as oil demand increases, and as the world gets ever more volatile, real intelligence will matter ever more.

You know how I can sit back and read your posts with humor and nonchalance?

Because I know that not only will you fail, but your children will fail, and everything you have built will die with you, because you don't believe in anything that's real.

REAL is that one person can know the truth and stand against the world and watch a world die.

You will not succeed with lies, and neither will your children.

But I will be here to watch it all, and when you are gone, I will still be here.

That's the power of mathematics.

That's the power of the truth.

Years ago I warned you and you've watched the world change, a prisoner to your betrayal, as the test was of mathematicians.

Now watch as the world finally feels the full taste of your failure, and watch as change is all that you see.

You will feel the punch of your failure, with the world that you betrayed.

And as you watch, you will begin to understand what truth is.

I have not defined truth, but you will feel it.

It will shred you and all that you know.

## SF: Definitely a new factoring method

Ok, so now wasn't that fun! Several years of effort with lots of very crappy and even stupid ideas under the bridge but now there is a new factoring method.

The method is given a target composite T, you can search for x and y such that

x^2 - y^2 = 0 mod T

by picking x_res and S, to solve for a variable k, where

k = S*(2*x)^{-1} mod T

and

x+k = sqrt(S+k^2 + y^2)

so finding x and y is just a matter of factoring S+k^2, so it is, indeed, a surrogate factoring method.

It has been shown to work by a Tim Peters, who has also been certain that it can't be made practical, but that is irrelevant to the question of it definitely being a new factoring method.

So even from the "pure math" aspect, the event here is significant.

The achievement was the result of lateral thinking, wondering if it might be possible to factor one number by instead factoring another, which I call surrogate factoring.

Surrogate factoring has been achieved.

The continuing debate is over its effectiveness.

I am no longer talking out research on Usenet.

I have contacted the U.S. military and we'll see how it goes. They may just think I'm a crackpot.

Others may feel free to play with these ideas as they see fit, as of course, I couldn't stop you anyway.

[A reply to someone who said that, even if it works, it will be useless if it is not efficient.]

That's a practical argument.

I'm making a "pure math" argument.

Besides, there are very few known factoring methods, despite what some of you seem to think from your replies to me, as if there are these things all over the place.

Look it up.

The achievement is fairly huge, whether it's practical or not.

New ideas are just not that easy to come by in modern mathematics.

I know a lot of you hate me, but reality is, what it is.

So a person you hate makes discoveries. Deal with it.

Or, you can choose to betray your discipline clearly in an area where there is no doubt what you're doing where I can maybe pull worldwide attention because of the status of the problem.

I don't care any more.

If you people wish to be one way with research from people you like and then another with someone you hate, then fine, I'll do my best to make sure you face consequences, as either you love mathematics, or you're liars anyway, who played a line that sounded good to you and the world.

## SF: What can happen, roadmap to my research

There was a story here recently in the United States about a woman killed by falling concrete in what's called the "Big Dig", where her husband escaped. They were just driving people. Neither of them expected one of them to die.

In constrast with my factoring research, if it is correct, some of you can expect a seriously negative impact on your lives.

So why sit like some poor frog in a pot of water that is slowly coming to a boil?

I suggest to you, you sit because it is human nature. In many ways, you are not different from a frog as your mind in this situation can't take the temperature.

You may survive, and someone you love may not, like that husband who escaped, but his wife was crushed, in a situation where they should have been safe.

The real world is an amazing thing. Things happen that you don't think can happen.

I am not a crackpot.

I am a major researcher who stumbled across massive failures within the modern mathematical community and rather than face their failures most of them simply sat, like frogs, waiting for the pot to boil.

Did any of you know that along the way of my research path at one point I contacted Barry Mazur about an argument that was later published in an electronic math journal, which retracted the paper when some sci.math people emailed them, and later the journal died?

Or did you know what when I sent that argument to the Annals of Mathematics in Princeton, and checked back with them six months later I was told that they emailed a rejection five months before, which I never received.

That's Princeton people. Claiming they sent an email is like some kid coming in and claiming that the dog ate his homework.

This story is bigger than any of you, and all of you.

And like that woman, you can find yourself in a situation that you did not ask for, as that's life.

Here's a roadmap of what I think of now as my major research to give you some grasp of what you are up against if you think that you can sit back and wait, as if nothing will happen.

When I say you are a frog, and the water is coming to a boil.

My research speaks for itself.

I have given a definition of mathematical proof:

http://mymath.blogspot.com/2005/07/definition-of-mathematical-proof.html

Figured out the key properties that define rings that are like the ring of integers:

http://mymath.blogspot.com/2005/03/object-ring.html

Found my own prime counting function, which unlike any other known relies on summing a partial difference equation, which is also why it finds primes on its own, unlike any other known:

http://mymath.blogspot.com/2005/06/counting-primes.html

Fighting mathematicians who have done their best to ignore my research I wrote the first prime counting function article for the Wikipedia, where my latest version is now found in the history of the current page:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&old...

There readers can see my prime counting function in its fully mathematicized "pure" form, and see how it is a summation, so they can make the leap to understanding how it relates to a partial differential equation and an integration.

I had a paper published in a formally peer reviewed mathematical journal—and then the editors withdrew it after sci.math pressure against it:

ttp://www.emis.de/journals/SWJPAM/vol2-03.html

Link is to a site mirror as the electronic journal DIED a few months later.

That paper covered some pioneering research advancing modular algebra or the algebra of congruences, extending on the work started by Gauss:

http://mymath.blogspot.com/2005/07/tautological-spaces-factoring.html

Which is a line of attack I used to find a short proof of Fermat's Last Theorem:

http://mymath.blogspot.com/2006/03/proof-of-fermats-last-theorem.html

But I've even considered problems in logic and set theory, handling supposed contradictions:

http://mymath.blogspot.com/2005/06/three-valued-logic.html

and

http://mymath.blogspot.com/2005/05/logical-formedness-axioms.html

and

http://mymath.blogspot.com/2005/06/3-logic-more-basics.html

Even some of my minor research is significant, as I talked about a simple way to find primes using quadratic residues:

http://mymath.blogspot.com/2006/04/method-for-quickly-finding-primes…

The only explanation given the breadth of my research, and dramatic events like a math journal imploding after publishing then retracting a paper of mine is that it is so huge that mathematicians who are living in a political society today—where their word is more important than their research—are fighting a war to deny acceptance of any of it.

If any piece of my research is acknowledged as important from my definition of mathematical proof to my ideas about finding primes then they have to fear that the world will realize what they are doing, so the math wars as I call them are political ones.

It is a fight of group power against mathematical truth.

## JSH: Continuing puzzle

Jealousy and envy are as old as humanity. It is not a surprise to me that other people would attack my ideas or claim things are false about my work, as why would they help?

What continues to puzzle me is, why does the world let them?

That is the puzzle that helps to fuel the gap—the time period during which I simply let my latest factoring ideas sit out there without forcing the situation—as consider!

If those factoring ideas are correct then people none of you know could lose their entire life savings, and those are people who are possibly responsible adults who care about their lives and their children—value their time and investments.

But right now, I have the power to end that, and the world is still giving me that power, while a few people attack my ideas, which doesn't surprise me, as why wouldn't they?

Nations can fall.

I am puzzled. Do none of you understand mathematics enough? Can none of you grasp the possibility?

Or is it that those of you who can want me to do it?

You pray every night that I quit talking and simply push forward to end the world as we know it?

It would explain the insults: goading me on, willing me to crush other people's lives, end the current system, break the world as it is.

But the time-table is set so goading doesn't change things, and the gap continues.

We march towards that which history has pre-ordained.

I don't know how long it will go on from here, but for now it continues, and I puzzle about the world ever more.

## SF: Considering possible solutions

I put up a simple idea for factoring where some may think, if they checked it at all, that they have shown it to not work well, so here's a post that might help.

x^2 - y^2 = S - 2*x*k

and use a technique where I pick the residue of x, so I use a congruence equation that has x_res instead of x, to choose S and k.

But imagine a solution for x^2 - y^2 that has T as factor where x = x_res mod T, but with a given choice for S, which has given you k by the methods I've explained in other posts

x^2 - y^2 > S - 2*x*k

for ALL solutions possible?

Necessarily then you get bumped to another residue. It's trivially obvious.

The simple solution is, get this, use a bigger S.

I now hypothesize that as T increases in size S will tend to have a size roughly equal to T by absolute values.

Now then, to let you get a sense of how solid this theory is at this point, imagine that the mathematics really doesn't care about the congruences I've found, and I'm just deluding myself, so let's consider a hypothetical solution for

x^2 - y^2 = 0 mod T

where x has, say, 1 modulo T as a residue.

Then

S - 2*x*k = 0 mod T

as well—because it has to from where I start—so then solving out I find

k = S*(2x)^{-1) mod T

just like before, as it's forced by the relationships.

So then, there IS a solution for the given S and k, in contradiction to the idea that the method doesn't work.

At this point then, the only possible objection might be that there is a narrow range for S?

So that the S you pick is only the residue there as well?

Maybe, so then it would turn into some search using S = S_res mod T?

Not likely, as T is likely to be big relative to its factors, so by that reasoning S might have to be truly huge relative to them, but why mathematically, when all that has to happen is that

x^2 - y^2 balances with S - 2*x*k?

Remember, problems with small S where you don't have a solution may simply be a result of it not being possible for the two sides to balance for a given solution with x having a particular residue.

And even if someone thinks that maybe S is just a residue, you're searching then modulo T for an S that works.

You're searching modulo T, the target itself, so if it's huge, the range of search is huge as well with every multiple of T you add to your starting S, but why would the mathematics force such huge numbers here?

I suggest to you that it only needs S to be roughly the same size as T.

## JSH: My research, a roadmap

My research speaks for itself.

I have given a definition of mathematical proof:

http://mymath.blogspot.com/2005/07/definition-of-mathematical-proof.html

Figured out the key properties that define rings that are like the ring of integers:

http://mymath.blogspot.com/2005/03/object-ring.html

Found my own prime counting function, which unlike any other known relies on summing a partial difference equation, which is also why it finds primes on its own, unlike any other known:

http://mymath.blogspot.com/2005/06/counting-primes.html

Fighting mathematicians who have done their best to ignore my research I wrote the first prime counting function article for the Wikipedia, where my latest version is now found in the history of the current page:

http://en.wikipedia.org/w/index.php?title=Prime_counting_function&old…

There readers can see my prime counting function in its fully mathematicized "pure" form, and see how it is a summation, so they can make the leap to understanding how it relates to a partial differential equation and an integration.

I had a paper published in a formally peer reviewed mathematical journal—and then the editors withdrew it after sci.math pressure against it:

http://www.emis.de/journals/SWJPAM/vol2-03.html

Link is to a site mirror as the electronic journal DIED a few months later.

That paper covered some pioneering research advancing modular algebra or the algebra of congruences, extending on the work started by Gauss:

http://mymath.blogspot.com/2005/07/tautological-spaces-factoring.html

Which is a line of attack I used to find a short proof of Fermat's Last Theorem:

http://mymath.blogspot.com/2006/03/proof-of-fermats-last-theorem.html

But I've even considered problems in logic and set theory, handling supposed contradictions:

http://mymath.blogspot.com/2005/06/three-valued-logic.html

and

http://mymath.blogspot.com/2005/05/logical-formedness-axioms.html

and

http://mymath.blogspot.com/2005/06/3-logic-more-basics.html

Even some of my minor research is significant, as I talked about a simple way to find primes using quadratic residues:

http://mymath.blogspot.com/2006/04/method-for-quickly-finding-primes…

The only explanation given the breadth of my research, and dramatic events like a math journal imploding after publishing then retracting a paper of mine is that it is so huge that mathematicians who are living in a political society today—where their word is more important than their research—are fighting a war to deny acceptance of any of it.

If any piece of my research is acknowledged as important from my definition of mathematical proof to my ideas about finding primes then they have to fear that the world will realize what they are doing, so the math wars as I call them are political ones.

It is a fight of group power against mathematical truth.

## JSH: The gap covers social reality

Can a short, simple and beautiful factoring approach be presented in our modern world with all of its connectivity and NOT be picked up by the mathematical community for a significant period of time, like several days, if that community is as brilliant as many people think it is?

I strongly suggest to you, no.

The thing is that I have several major mathematical finds and have fought a long and hard battle against the real mathematical community, which in my experience doesn't give a damn about mathematical proof and easily lies about things mathematical.

But how do you prove that?

If I just put forward a full implementation of a factoring solution and make certain there is evidence that even non-mathematicians would accept immediately OF COURSE the mathematical community would jump on board—just as fast.

But my point is that the current mathematical community is no better than the lay community when it comes to mathematics, and in fact is worse, as it actively fights correct and important mathematical results.

I'd have no chance if the factoring problem weren't connected to trillions of dollars.

No chance. You people would just ignore this research like all the rest, and some of you would call me names, call me a crackpot, and a crank.

The time lag that is currently taking place—the gap—is incontrovertible proof that your community is not what it pretends to be, that you are pretenders, lying about your actual mathematical abilities and inclinations, and willing to sit quietly, on world shaking mathematical finds.

## JSH: Another possibility

But it occurs to me that you people aren't really that dumb about mathematics and so unbelieving of mathematical proof that you think you can just wish away a mathematical result, or just say no, no, no.

Another more sinister possibility occurs to me which is that you actually thought you were part of some great conspiracy, so you expect some powers from somewhere to swoop in and make me disappear.

You poor people deluded yourselves probably believing that no one could find a short proof of Fermat's Last Theorem or the prime counting function I found or have any of these other major results and not get recognition unless it were part of some massive conspiracy.

But it wasn't.

My analysis is that some mathematicians at the top chose to sit quietly quite deliberately, but that most of you simply looked around, saw no one else reacting, and followed the crowd.

Simple human behavior people. No great conspiracy.

No one to save you here at the end. No secret government agency to sweep in out of the blue.

No one to back you up and make this story just disappear.

You will face the world, and the world will know what you and your community has done.

The gap is nearly complete.

The government agencies WILL come in soon enough, but they will come in investigating you people.

## JSH: My working theory on the psychology

To me mathematics is about the search for truth as the highest ideal, and a mathematical proof is a part of the ideal of truth as it is perfect, absolute, inviolable.

A mathematical proof is just true, no matter what, and cannot be broken, tarnished or made false.

A mathematical proof is an absolute outside of time.

So I wonder about people lying about mathematical proofs, and the explanation I'm working on now is that for many of you, everything I said above is foreign.

And I don't think you believe it.

So to you a mathematical proof is a human construct that can be broken or malformed, or may be true one day and false the next, and your view, I believe, is that most importantly proof is what people BELIEVE to be true.

That would explain how people could keep lying about my research, I think, as some part of them may think that if they just keep saying it's wrong enough times, it may be wrong, as if there is some changeable thing about the research.

In reality, my past mistaken ideas—when I thought I had proofs and did not—were just wrong, and never right. Correct ideas of mine, are just correct, independent of me.

I have no impact on the truth or falsity of even my own ideas.

Their truth value stands one way or the other—true or false—without regard to me, at all.

That reality is what seems to be missing from the mental paradigms that many of you are clearly using.

For many of you, I believe, there are no absolutes, not even mathematical proof.

While to me, there is nothing outside of mathematical proof, so with us inside of it as well, no thing stands apart from absolute truth, not even nothing.

## Simple factoring result, but what about lies?

I put up a post yesterday about how loose connectivity from using congruences works with these simple equations to produce an approach to the factoring problem.

You can read my posts on the subject and at least one other post from someone else has appeared in the thread.

I have posted on this subject at other newsgroups and there have been people who have similarly posted in reply simply declaring things about the method, or even being derogatory to me.

Now my question to you is, but what if I am right and this is some significant mathematics, how do you explain such behavior?

I'm puzzled by the behavior, so I'm looking for input on why people would behave this way.

I DO have other mathematical research, which is quite solid and have faced lies about it, but in "pure math" areas where I could not get anywhere past such behavior. Here with the factoring problem, of course, that behavior is not as powerful, but I'm curious about why ANY person would behave in this way.

Any clues?

The problem I have is this is just one of my major mathematical results.

If it IS a solution to the factoring problem and I just create a factoring algorithm and implement it, proving that beyond a doubt in a rapid period of time, then mathematicians who by now should know about the theory, would, of course, jump up and down proclaiming the greatness of the solution!

That makes it easy for them.

But now there's just the beautiful mathematics—pure and simple.

Anyone with a modicum of knowledge about algebra and factoring knows that it's new, but they can look around and see the mathematical world doing nothing, while a few posters poke fun at the idea.

However, it is a contradiction for brilliant and beautiful minds to do nothing when faced with a simple factoring solution with very clear mathematics and theory, so those who are doing nothing—waiting to see what happens—are not such minds.

So the time lag is the proof I need to keep mathematicians from coming up later and just claiming they didn't have a chance, while I'm sure plenty of them will claim to not know about it, and probably most of them don't, but even that is a dramatic demonstration of the failures of the society.

I have been posting on sci.crypt, sci.math, alt.math, alt.math.undergrad, and alt.math.recreational and if there is NO ONE on any of these groups who picks up on a dramatic theory with such implications, then isn't that a proper indictment of mathematical society?

Just to be sure, I'll probably email it to some major mathematicians as well, if that becomes necessary and the time lag continues.

The proof here is that mathematical proof isn't what matters to these people—they're looking for social reaction.

They are political animals in a social situation, not true mathematicians, and not "beautiful minds".

## JSH: So how can they lie about math?

I am desperately in need of understanding how some people can lie so easily about mathematics, so they reply to me as if it only matters that they disagree!!!

Of course with my other research that could be effective.

But how could anyone reasonably expect simply disagreeing with me and calling me names to stop people from noticing a possible solution to the factoring problem?

What kind of thought process is going on here?

I do know that some mathematicians show signs of mental breakdowns when confronted with my proofs in such a way that they cannot simply deny.

Is that it? Simply some kind of bizarrre mental break?

How long can it last? And what happens when mathematical reality and social reality—as the factoring problem is of major social importance to the point that lies of this type cannot long succeed—forces through?

Actually the behavior is like that of an angry child in this case.

Some kind of reduction to the infantile by the pressure of the results?

But why exactly?

And why would this poster think his behavior ok on this forum?

Is it not at least somewhat embarrassing?

The discussion is in no way like that of adult conversation. I think that is at least quasi deliberate, but maybe it is more real than the poster is willing to admit?

Possibly my research makes others feel less about themselves?

[A reply to someone who said that james had insulted everyone in the sci.math newsgroup.]

Everyone? How do you know I didn't miss a person here or there?

That's not really meant to be humorous as your use of the word "everyone" is so obviously non-logical that it perturbs me.

What deludes you to think that you've covered everyone in this newsgroup?

I present proofs. I found that in arguing out proofs I'd get replies that simply ignored them, or lied about them, while the group went along.

Even getting a paper published wasn't enough to stop you people.

You simply used social forces against the publication and then rationalized that it happened.

But you can lie about a factoring result, rationalize, ignore it, or politicize it and it just won't change the reality that if it is correct it will eventually get picked up and used by people who will recognize it as correct.

The mystery to me though is how do you maintain this behavior?

What are you gaining from it anyway?

I'm puzzled. While I'm puzzled and the gap is spinning out, there is time for you.

When the gap is complete, then something should happen…

[A reply to someone who said that nobody has ever verified James' work as correct.]

That's not true. I even had a paper published in a peer reviewed math journal—the journal later retracted—after some sci.math'ers sent some emails claiming it false, but it was peer reviewed and verified.

Also I have research that no one claims is incorect like my prime counting function.

You aren't really worth replying to, but my problem is that people like you make statements like that and you're believed.

It's a sad state of affairs but it's why this is a war—the math wars I call them—as it's a political war where I face people who say false things about my research—and are believed.

These math wars will go on until I break math society, or it quits playing politics with mathematics.

At the rate things are going, it will probably be me breaking the society completely, as I see little evidence that mathematicians have given up on the political tools they obviously treasure—so I will have to prove to them what mathematics truly is and how powerful it actually is, over social stuff—and then I will sweep through cleaning house and that should end the politics, at least for a while.

[A reply to someone who said that the paper was “withdrawn” and that this means it was found full of mistakes.]

Nope. The chief editor Ionnis Argyros just yanked it immediately after he got emails that sounded good to him. I communicated with a colleague of his by email and that person also an editor said that he'd had cases of reviewers who screwed up, and probably Argyros figured that's what happened. Remember the sci.math people emailing him were putting Ph.D in mathematics in their emails. And, um, yeah I guess they have them, but still, that's more than enough intimidation, but still Argyros should have held a bit.

But he knew I was just an amateur as I told them that before they published, and with Ph.D's in mathematics emailing him like that, why wouldn't he have a serious gut check?

He just pulled it at first, leaving a gap, so the page numbers didn't work right, so they put in various things, until they settled on "Withdrawn" which is unfortunate as some may think I withdrew it, when I did not.

The journal managed one more edition before it quietly shut down—dead as a freaking dodo.

So part of this saga is a dead goddamn math journal.

The story doesn't end there as the Annals of Mathematics makes a freaky appearance later on, but that's another tale, for another post…

## JSH: Way too interesting

So I have this neat result using congruences which is so easy and trivial that I can just put it out there and watch what happens!

And on this group, surprising even me, there is still the usual reaction.

I can check with other groups and see what happens, shifting how I present the mathematics.

Far more interesting than I thought possible.

It's like a study of the world with the most powerful intellectual microscope ever built—a simple solution to the factoring problem versus a social view that I'm just some crackpot

[A reply to someone who said that James doesn't a microscope to do that.]

I am curious about the type of thinking that would allow the denial of my research for over 4 years, as can it just be as simple as a person like yourself knowing the truth but just lying about it?

I would like to think, no.

So, for some reason, you believe that I am wrong, but why?

And now with a result that cannot be long denied because of its practical relevance, whatever rationalizations you have used to justify your behaviour SHOULD I would think, collapse.

Yet here you are, still posting in defiance of that analysis.

## Loose connectivity, factoring and residues

The factoring problem can be easily approached using simple algebra.

x^2 - y^2 = S - 2*x*k

where all are integers, as notice then you trivially have

x^2 + 2*x*k + k^2 = y^2 + S + k^2

so

x+k = sqrt(y^2 + S + k^2)

and finding y is just a matter of factoring (S+k^2)/4.

Now with just the explicit equation you end up with nothing but trivialities, but turning to congruences, you can now simply let

x^2 - y^2 = 0 mod T

which—this is important—now forces

S - 2*x_res*k = 0 mod T

where I put in x_res to emphasize that now it's congruences, so there is loose connectivity and an explicit value of x is not needed—just a residue.

But now I can just solve for k, assuming 2, S and x are coprime to T:

k = S*(2*x_res)^{-1} mod T

where (2*x_res)^{-1} is the modular inverse of (2*x_res) mod T.

That the modular inverse makes an appearance is critical, but more importantly I now have a way to find all the variables!!!

That can be done by simply picking a residue for x_res and then picking S, like x_res = 1, and S =1, to get k.

For instance if T=35, and I use x_res=S=1, then k = 18 mod 35, and k=18 will suffice.

Then y is found by factoring (1+18^2)/4 and then you have x as well.

Of course there will exist and x and y such that

x^2 - y^2 = 0 mod T

for any x_res you choose, which is trivial to prove, as that is equivalent to

x^2 - y^2 = kT

where k can be any integer.

So an equation that is useless explicitly becomes quite powerful with modular algebra—introducing loose connectivity—leading to a general method for factoring.

## Factoring and residues

Can you figure out something wrong with the following?

x^2 - y^2 = S - 2*x*k

You can solve for x and y in terms of the other variables easily as that is just

x^2 + 2*x*k + k^2 = y^2 + S + k^2

so

x+k = sqrt(y^2 + S + k^2)

and finding y is just a matter of factoring (S+k^2)/4.

But get this, now I just let

x^2 - y^2 = 0 mod T

then

S - 2*x_res*k = 0 mod T

where I put in x_res as I don't know x, so I'm using its residue.

So x_res = x mod T, and I can solve for k, assuming 2, S and x are coprime to T, with

k = S*(2*x_res)^{-1} mod T

where (2*x_res)^{-1} is the modular inverse of (2*x_res) mod T.

So just pick some x_res and S, and find k, which now allows calculation of y, and x.

Of course there will exist and x and y such that

x^2 - y^2 = 0 mod T

for any x_res you choose, which is trivial to prove.

So it looks like there is this almost impossible to believe simple answer to it all.

So what's wrong with the above?

## JSH: Surprised even me

You people are totally incompetent.

All these years I thought that at some level maybe some of you knew mathematics, but now I see you don't.

I am actually silly enough to still be further disappointed.

You people have no real interest in mathematics.

You are play-acting a role of what you think a mathematician would be like, but if Gauss were alive today, he would not talk to any of you, I am sure.

I was working at hard problems, actually discovering mathematics, so my attention was always somewhat diverted, and the energy I directed against any of you was always muted.

You do not know me, or what I can do. You clearly have no clue about what it is like to face a real mathematician in his own domain.

And now I get to concentrate on taking you apart versus dealing with the hard world of discovery.

And I have no compunctions against repeatedly stripping you all of your illusions.

Remember, part of my goal is to shut down entire math departments.

I need you help to accomplish it. I need you to behave as you are now, as the anti-mathematicians you are.

Without your help in avoiding powerful and simple mathematics, I can't toss out people like Barry Mazur or even Andrew Wiles.

I need your simple faith in social ways against mathematical proof to build the energy.

I need what you are doing now.

## JSH: Bunch of actors

The key to my beating you people was figuring out that you were just a bunch of actors.

It took years for me to realize it, as I kept thinking that there was some substance to modern math society somewhere, but it finally settled in, there was not.

So now, you think you can just talk your way out of a solution to the factoring problem.

Fine. Try it. See what happens.

## JSH: Now what?

Kind of one of those odd things, but this idea just did come to me Saturday in that I just wrote down some equations and hey! I solved the factoring problem.

It's a quadratic residue solution, which may have been helped along by Tim Peters noting when talking about a previous failed attempt that if you could get multiple quadratic residues that were equal you could factor.

He claimed it was a hard thing to do.

At the time I thought to myself that I didn't think it was, but I didn't know how to do it.

That though may have lead my mind down the paths that eventually caused the solution to just kind of pop out fully formed.

So one way to look at what I found is that I came up with a way to get a lot of equal quadratic residues.

The proof is trivial.

The impact is not.

So why post it?

I've talked about that before, and maybe at this point the real answer is that I've been wrong so many times that part of me still doesn't believe it here, even though I think I have the proof as I've thought that before and been wrong.

So I don't want to invest myself in the damn thing beyond the usual ways—posts!!!

If it's right, well, well, I think it is right, but this situation is just so wacky anyway.

I've been looking for federal people all day, expecting the FBI or even maybe someone from the NSA to show up, but nothing…

But it's such a natural, simple solution that in retrospect is obvious. It's also kind of clear why most people wouldn't go down those paths, as I am a lateral thinker, trained in it very well.

I did something that I think most would consider unnatural, and that's what it took.

So the short answer is that the question of how to get a bunch of quadratic residues of equal value is done. That answer leads to a factoring method. That factoring method should be a solution to the factoring problem.

And it's very short, very straightforward, and so it should be unbelievably fast.

Now what? I don't know. I kind of wish there had been another way to go, but the fact that I posted this thing on Usenet yesterday, even though it was on sci.skeptic, and nothing has happened up until today shows how mucked up the math community is.

You people have to be banged on the head and forced to look at even simple proofs of famous problems.

It's weird. It's like, you can't just look and get it. Someoe has to push it on you, and hammer, hammer hammer to get you to pay attention till MAYBE you'll think that possibly there's something there.

Which to me sounds like you're not really the mathematicians some of you seem to think you are.

While I find these things in the wild.

## Let's play what if, factoring problem stuff

Yesterday I decided to put up my latest factoring ideas, which just came to me Saturday, when I've been searching desperately for something with financial significance because the math community has succeeded in not properly acknowledging my other research.

Well, what if what I presented is correct, and blows the factoring problem apart?

You don't need to know any mathematics to consider the questions in this post, as I'm just wondering as I get more and more bemused by the situation.

Remember, I've gone after the factoring problem to find something mathematicians couldn't ignore, and had lots of failures.

This weekend I had this amazingly simple idea which I think—though I haven't tested it yet—might actually be something of a miracle solution in its simplicity.

I have posted it on Usenet.

Nothing so far has happened.

Does that say anything?

Would it change your opinion of the math community if it turns out I'm right and I could just post a billion dollar plus solution and days go by?

Does it bug you that maybe right now on your forum there is this answer that anyone in the world might use and maybe snoop on your financial transactions over the Internet, or break into your cellphone?

Or do you figure there is just no way in our modern world that could happen that a solution could just be sitting out in plain sight with NO ONE doing anything about it?

I should test it, but I am desperate. If I test it and it doesn't work, I lose hope in an impossible situation. So I consider the idea and the ramifications, but what if I'm just wrong, and that thing is just some crap math?

I test it, and I find out. While I don't have test results, I can speculate, and pose questions.

## JSH: Is it possible?

I say that the math community is corrupt and inept, so to me it's quite possible for a simple solution to the factoring problem to be presented to members of that community on Usenet, and the damn fools not get it.

Is it an excuse that I had lots of failures before that I thought were solutions?

Or, if the math community is at all competent, should it be able to tell a solution when it sees one, no matter how many failures preceded it?

I think a lot of people play at being mathematicians with no real clue about what it really means to be one, so, yes, they can see a dramatic and simple solution to what was thought to be a great problem, and it just sail right over them.

You need to adjust to the mathematical reality.

The proof is right there in front of you.

That I'd win at the end in this way maybe too much for your mind to take.

But that's what happened.

The math wars are over.

[A reply to someone who said that the mathematical community would be able to say whether or not a possible solution is indeed one.]

But what if you didn't? What would that mean then?

Would it really be some random thing, or such a huge miss that it can only mean one thing?

Like if a pro baseball player can't catch an in-field fly?

Maybe he's not really a pro?

If you people can have a dramatic and short solution to a problem worth hundreds of billions of dollars to the world right in front of your faces and not see the damn thing, what good are you really as mathematicians?

What good are you to the world if you fail with something easy AND important?

Maybe then, you're just fakes? Maybe you're actors playing at being something so far beyond you that you can't see simple stuff?

Maybe you're just about style with no substance?

## Factoring and residues

Can you figure out something wrong with the following?

x^2 - y^2 = S - 2*x*k

You can solve for x and y in terms of the other variables easily as that is just

x^2 + 2*x*k + k^2 = y^2 + S + k^2

so

x+k = sqrt(y^2 + S + k^2)

and finding y is just a matter of factoring (S+k^2)/4.

But get this, now I just let

x^2 - y^2 = 0 mod T

then

S - 2*x_res*k = 0 mod T

where I put in x_res as I don't know x, so I'm using its residue.

So x_res = x mod T, and I can solve for k, assuming 2, S and x are coprime to T, with

k = S*(2*x_res)^{-1} mod T

where (2*x_res)^{-1} is the modular inverse of (2*x_res) mod T.

So just pick some x_res and S, and find k, which now allows calculation of y, and x.

Of course there will exist and x and y such that

x^2 - y^2 = 0 mod T

for any x_res you choose, which is trivial to prove.

So it looks like there is this almost impossible to believe simple answer to it all.

So what's wrong with the above?

## Real world test, factoring problem

In desperation over the math community's ability to ignore my research I have for some years been searching with little success to find some answer to the factoring problem, thinking that would be research mathematicians couldn't get away with ignoring.

I've been at it more than ever lately with a lot of frustration and failure, but I had this simple idea that just kind of came to me Saturday, but I am afraid to check it.

It represents hope for me, and checking it and finding it wrong, would mean I was still desperate, still searching with very long odds for a way of climbing out of my Hell.

But maybe it's right? If so, there's no way it can be ignored for long, right?

Here it is.

I started by just out of the blue writing down the following equation:

x^2 - y^2 = S - 2*x*k

You can solve for x and y in terms of the other variables easily as that is just

x^2 + 2*x*k + k^2 = y^2 + S + k^2

so

x+k = sqrt(y^2 + S + k^2)

and finding y is just a matter of factoring (S+k^2)/4.

But get this, now I just let

x^2 - y^2 = 0 mod T

then

S - 2*x_res*k = 0 mod T

where I put in x_res as I don't know x, so I'm using its residue.

So x_res = x mod T, and I can solve for k, assuming 2, S and x are coprime to T, with

k = S*(2*xres)^{-1} mod T

where (2*x_res)^{-1} is the modular inverse of (2*x_res) mod T.

So just pick some x_res and S, and find k, which now allows calculation of y, and x.

If that idea is solid then they can't ignore it, right? The mathematicians can't fight something that has monetary value, right?

## My central disappointment

I talk about problems that I think are in modern math society or about what I say are my own mathematical discoveries that are being ignored, but what really bugs me is the inability to get support after explaining the situation.

There are any number of dramatic elements to the story, and facts that lead credence to my position, like that electronic math journal that published one of my papers, withdrew it after some emails from sci.math people falsely claiming error, and then only managed one more edition before dying.

Or how I wrote the first prime counting function article for the Wikipedia.

My wide mathematical interests don't fit into the box for a "crackpot" so math people just act like I talk about only one thing: Fermat's Last Theorem. As you can see by doing a search on "James Harris", just to see how big their opposition to me is, and wonder about why.

If I am just some crackpot, why all the energy?

If you dig into what my paper that got published was about you find out that I discovered an odd flaw in some very old mathematical ideas—ideas that go back over a hundred years—and acknowledging the flaw could be a major embarrassment to the mathematical community.

So I can show my mathematical arguments. Give dramatic demonstration that at least some mathematicians accepted them—enough to publish a paper—and give motive for other mathematicians to fight my research.

That journal may have died because the editors did believe my paper, and faced with fighting to push the result, or continue to publish research dependent on the flawed ideas—they decided to shut-down, which is speculation on my part.

What is not speculation is that I had a paper, I had that paper published in a math journal, and after withdrawing my paper under pressure from sci.math people who sent emails, the journal died.

I find it remarkable in this day and age that so many people can listen to my story, and do nothing constructive to help the situation.

Yet without mathematics you would not have this technology. We would not have the scientific advancements we do. And our civilization would not exist.

I've heard people I've explained my situation to, say that often people are not recognized for their accomplishments until long after their deaths, as if I'm destined to be this tragic figure.

But hey people, now I am alive, and I don't like accepting this calm acceptance of my failure up until death to be recognized for my discoveries.

It may be easy for you to think about me not being known for my discoveries until after my death, but to me, it's an unsettling and very much undesired outcome.

So I have a disappointment in intellectual society that such a dramatic story could happen in our modern age, and so many people just quietly decide that it's not their problem, and leave me to figure out a way to resolve the situation.

Where are the intellectuals? Where are the thinking and caring adults?

Where is our brave new world?

## Some perspective, math society

Now I think a lot of you may want to naturally side with the math community when it comes to hearing someone like me warning that hey, maybe something is wrong there, but here's a quick thing you can do:

Do a search on "James Harris" in Google.

Search on my name and in the top ten you will see a link to a Crank.net webpage where I'm excoriated as a "loon", "crackpot", "crank" that bugs the sci.math newsgroup with supposed proofs of Fermat's Last Theorem.

So I'm in the top ten for James Harris's in the United States—according to Google—for bugging math people on Usenet.

If you look at the page, you may think that I spend a lot of time on Usenet talking about Fermat's Last Theorem, but I don't. I used to, as for years I looked for a simple proof, and thought I had one a couple of times, when I didn't. And later I found something that I'm sure is a short proof (though not so simple) and with it in hand, I don't talk about it much.

Why bother? I moved on to other things.

But the page didn't change, and for de-bunking links you can see the dates for those webpages.

It appears to me that the owner of the website has no intention of ever updating the page with facts, but feels quite comfortable presenting me as being someone arguing about Fermat's Last Theorem, indefinitely.

That's the math society I see.

Why bother with the facts when you can play politics?

It's just too freaking inconvenient for that guy maintaining the page to keep up with my mathematical interests, so he just picked one thing, and sits with it—for years.

Like, who gives a damn about the truth?

Cons don't work hard people. That's why they're cons. People who work for a living don't need to cheat. And math people aren't forced to work hard by a public that either fawns over them as "beautiful minds", is terrified of mathematics, or just doesn't know who the hell they are, or care.

But mathematics is so important to our world that without it, the science and technology we have today would not exist.

[A reply to someone who told James that his parents should be proud of him.]

And you just scoot past the oddity of it all.

Why such a big reaction from the math community?

I've found cases of other people with the name "James Harris" having to tell people they are not me.

How is it that I'm such a big deal, but you have someone like the owner of Crank.net trying to say that my research is not important?

Mathematicians do have a system that relies on the word of other mathematicians in areas they call "pure math", which means that they can as a group declare things to be true, whether they are or not.

IN a political world, politics rule.

They play politics with me because they always play politics, so it's second nature to them, and trying to put a nasty spin on the name "James Harris" is nothing to them.

The math world is not what you think it is, and they don't play by the rules that most of civilized society follows.

## SF: Better exposition of new factoring idea

Thought I'd make a cleaner post without errors showing this simple factoring idea that I just figured out a couple of days ago.

It IS surrogate factorization which can be seen from the start, as S+T is the first factorization equation shown, and the math is straightforward from there:

x^2 - a^2 = S + T

and

x^2 - b^2 = S - k*T

I could subtract the second from the first to get

b^2 - a^2 = (k+1)*T

which is, of course, a factorization of (k+1)*T:

(b - a)*(b+a) = (k+1)*T

with integers for S and T, where T is the target composite to factor, so you have to pick this other integer S, and factor S+T.

Really simple.

But how do you find all the variables?

Well, if you pick S, and have a T you want to factor, then using

f_1*f_2 = S+T

it must be true that

a = (f_1 - f_2)/2

And

x=(f_1 + f_2)/2

so, you need the sum of factors of (S-k*T)/4 to equal the sum of the factors of (S+T)/4, so I introduce j, where

S - k*T = (f_1 + f_2 - j)*j

and now you solve for k, to get

k = (S - (f_1 + f_2 - j)*j)/T

so you also have

S - (f_1 + f_2 - j)*j = 0 mod T

so

j^2 - (f_1 + f_2)*j + S = 0 mod T

and completing the square gives

j^2 - (f_1 + f_2)*j + (f_1 + f_2)^2/4 = ((f_1 + f_2)^2/4 - S) mod T

so

(2*j - (f_1 + f_2))^2 = ((f_1 + f_2)^2 - 4*S) mod T

so you have the quadratic residue of ((f_1 + f_2)^2 - 4*S) modulo T, to find j, which is kind of neat, while it's also set what the quadratic residue is, so there's no search involved.

The main residue is a trivial result that gives k=-1, but you have an infinity of others found by adding or subtracting it from multiples of T.

It was pointed out to me that these are also trivial, so I figured out a way around that by turning the problem around a bit:

One approach is to find some quadratic residue r, where

(f_1 + f_2)^2 - 4*S = r + n*T

where n is a natural number, as then solving for f_1 gives

f_11 = (sqrt(4*S + r + n*T) +/- sqrt(r + (n-1)*T))/2

so you can arbitrarily pick some integer w, square it, and get the quadratic residue modulo T, which is then your r, so now you have

w^2 = r + (n-1)*T

so you can easily solve for n, and then you pick S so that the second square root is an integer.

So now you have

2*j - (f_1 + f_2) = w

is a solution.

Neat!!! I like solving problems!!!

Tell me more!

Now you can get k.

And then you can find b, from

b^2 = x^2 - S + kT

and you have the factorization:

(b-a)*(b+a) = (k-1)*T.

It is possible to generalize further using

j = z/y

and then the congruence equation becomes

(2*z - (f_1 + f_2)y)^2 = ((f_1 + f_2)^2*y^2 - 4*S*y^2) mod T.

If you're skeptical you may consider the question of finding k when you already have the factorization of T.

I've been thinking about this and looking at it, and it looks like factoring is easy—if you know how to do it—where the lateral thinking step needed was to start with equations factoring your target added to something else.

Weird. I wonder why Gauss didn't think of this?

It is a bit harder than I first realized though.

Hey, do you people think that maybe sitting quiet may be like being a frog sitting still in a pot water that is on a fire?

Did it ever occur to any of you that I've had over three years to get rather pissed off, since you people blocked my other research, like my proof of Fermat's Last Theorem?

I WILL empty entire math departments, maybe starting with Princeton.

## Assessing the modern math world

One of the stories that should be about to come out is the reality that I am not some "crackpot" but am a major discoverer who has been in a pitched battle against a mathematical community dead set on blocking knowledge of my mathematical accomplishments.

So I picked a problem they'd have trouble getting away with lying about—the factoring problem.

For those of you who don't know, the factoring problem is generally believed (for a little while longer) to be extremely difficult, so modern security systems are built around it.

I now strongly believe that it is trivially solved and now am considering the question of why the modern mathematical community spent so much time telling people they were safe with a flawed approach.

My opinion is that mathematical discovery is hard, few people come up with ideas at the level like I just did in coming up with my factoring idea, but LOTS more people want the title of mathematician than can actually be a real mathematician, and if you get enough people together working at something, they can come up with a flawed solution.

I suggest to you that modern "mathematicians" realized they could just write papers that LOOKED mathematical, SAY as a group the papers were correct, and it not seem to matter if they actually were.

So they came up with "pure math" which by being useless in applicability was perfect for their needs, as if no one could ever test the math in the real world, it couldn't be shown to be crap.

And that way all these people who could never be mathematicians if they had to come up with new and important mathematical insights, and have perfectly correct arguments, could still take the title, get the paycheck in some cases, and teach students.

They could have careers as mathematicians.

My guess is that the world may have about a hundred real research
mathematicians—if even close to that many as I'm being generous.

That probably is about all that would be born with this number of people on the planet, and that may seem low, but mathematical discovery is just a hard business.

With room for maybe a hundred real mathematicians, there is a lot of pressure from the wannabe's to just take over, and crowd real mathematicians out.

Like they came after me when I made my discoveries.

Of course there is a lot more room for people who TEACH mathematics, so there can still be thousands of people in the math field, who could teach and do scholarly work.

But there will probably never be more than a hundred—if there are that many—real research mathematicians capable of doing significant research.

My hope after this massive debacle plays its way through is that the lesson is learned that you can't just trust people.

You need objective checking. You need to look for danger signs from a community.

And you need to understand that mathematics is VERY important to our world, and also VERY difficult when it comes to original and important research.

Since people at my level come around only every couple of hundred years or so, it's easy for people to forget what we are like, and too easy I think, for pretenders to take over and crowd out the real researchers.

Which forces someone like me when I arrive to clean house, which can get very, very, very messy.

And not just messy for mathematicians, as many of you will learn, but without such work, civilization itself is in danger, and the future of humanity is at risk.

My role is something many of you will find impossible to fully grasp, so don't worry yourselves too much about it.

Let's just say, I am here to set some things straight in the mathematical field.

The pathos is a result of a situation unlike one most can imagine, where my remarkable accomplishments have been fought by a mathematical community which contradictorily shows it despises mathematics.

To prove that I am telling the truth I've focused on an area where they can't lie, and found an incredibly simple way to factor.

And they are quiet about it so far from what I've seen.

If you have a hint of a clue that I am telling the truth I suggest you prepare yourself for the worst case scenario, though I hope it won't occur. Stock up on supplies. Shift funds out of areas vulnerable to a melt-down if it turns out that the entire Internet has to change, forcefully, overnight.

Make sure your social networks are refreshed, and if there's someone you have been putting off talking to or spending time with, do it now.

The world you knew is about to end, and while I don't want to be too doom and gloom as the benefits to society are going to be immense—eventually—I do want those of you smart enough to listen to me, to have your chance to prepare.

The wait is nearly over—prepare yourselves.