Saturday, March 31, 2007
Factoring more beautiful now
The reality of the mathematics of what I've recently discovered is so simply beautiful. Succinctly for EVERY composite factorization by a difference of squares you have an alternate factorization automatically given as well:
x^2 = y^2 mod T
algebraically forces
S = (α + 1)k^2 mod T
where
α*k = 2x mod T
so α*k is set by your factorization, but you have an infinity of alternates available for α and k individually.
That is not in debate, and it is beautiful mathematics in and of itself which expands the factoring problem outside of what was previously known as mathematicians of the 20th century primarily labored developing various techniques to find a difference of squares where the most advanced known today is the Number Field Sieve.
I've mostly focused on the second factorization as a way to find the first, calling the technique surrogate factoring, but the mathematics offers more than one way to use this knowledge, and just yesterday I figured out yet another way to use the connectedness of factoring.
With that way I use a difference of squares of the surrogate, and then search for
(α + 1)k^2 mod S = 0 mod T
where I found a very easy way to do that, so that now you can deliberately set out to find a difference of squares, easily, with a straightforward method, for any composite that you choose.
My previous post on the subject was flawed—I'd just come up with it so mistakes are not a surprise—so to get the latest corrected the best thing is to go to my Extreme Mathematics group:
http://groups.google.com/group/extrememathematics/web/another-page-more-surrogate-factoring
It is such beautiful and simple mathematics that it is a shame that there is so much other surrounding this and I freely admit that I came to factoring primarily to force mathematicians to acknowledge my mathematical discoveries.
I found a proof of Fermat's Last Theorem, THE prime counting function, which not only offers a way to disprove the Riemann Hypothesis, but also tells 'why' prime numbers distribute as they do. I've given the definition of mathematical proof. And I cleaned up some areas in logic, explaining how logical form is crucial.
My research is defined like this latest factoring research by its simplicity.
In contrast modern mathematicians have work that is often complex, difficult to understand, and that is a technique to hide the reality that much of it is wrong.
Their research is so abstruse not because mathematics forces it so, but because by making it so, they can hide that it is not correct.
I have come to the sad conclusion that much of that is deliberate.
Because I am someone who breaks their way to make money, modern mathematicians are quite willing to ignore my research and try to continue their scam.
Mathematical research is difficult. It is easier for groups of people to play at being mathematicians than to be real ones. People like me emerge rarely.
But the greatest proof of the lack of real intellectual ability of those in the mathematical community who fight me is that fight.
They can't win. No one has won against someone like me. If they had our world would not be as it is, if Newton had been beaten, or Archimedes, or Einstein.
So factoring is the way to beat them. They will fight still because they're not smart enough to quit and later they will beg the world for mercy.
But remember, they sought to cut the jugular of the world. They sought to end the progress of the human species itself.
They sought to end us all no matter what they claim later.
They tried to make your life meaningless, to take away the future of your children, and to make the sacrifices and efforts of all those who came before us…meaningless.
[A reply to someone who wanted to know more about how James had explained “how logical form is crucial”.]
"Liar's Paradox". I showed how it's about form and is just about a need for a 3 logic, as the "law of the excluded middle" is no law at all.
I think it telling though that modern math people can turn successes like mine into a joke, or claim I do, because they have figured out a style.
Today people think they know what important mathematics looks like, and they think they know how people with correct mathematics should act.
But it's not a big deal now as that's why I went to the factoring problem, where the latest results are just so beautiful and amazing.
IN ways I feel sorry for modern "mathematicians" many of whom were brought into the field after it was corrupted (assuming that really happened in the latter 20th) and taught style as substance and trained to believe that being correct in mathematics is about being believed to be correct by your peers.
It's almost ludicrous to look back at how often these people would call me names or claim that no one believed me as if they had trumped me with the maximum!!!
To think, not being believed, how could I go on? LOL.
Well because most people don't know squat about math and lots of people get even basic things wrong, and, oh yeah, people do lie.
These losers just lie about math. From the proper perspective they just join a long line of people who pretended to be something they are not for personal gain, at the expense of others.
x^2 = y^2 mod T
algebraically forces
S = (α + 1)k^2 mod T
where
α*k = 2x mod T
so α*k is set by your factorization, but you have an infinity of alternates available for α and k individually.
That is not in debate, and it is beautiful mathematics in and of itself which expands the factoring problem outside of what was previously known as mathematicians of the 20th century primarily labored developing various techniques to find a difference of squares where the most advanced known today is the Number Field Sieve.
I've mostly focused on the second factorization as a way to find the first, calling the technique surrogate factoring, but the mathematics offers more than one way to use this knowledge, and just yesterday I figured out yet another way to use the connectedness of factoring.
With that way I use a difference of squares of the surrogate, and then search for
(α + 1)k^2 mod S = 0 mod T
where I found a very easy way to do that, so that now you can deliberately set out to find a difference of squares, easily, with a straightforward method, for any composite that you choose.
My previous post on the subject was flawed—I'd just come up with it so mistakes are not a surprise—so to get the latest corrected the best thing is to go to my Extreme Mathematics group:
http://groups.google.com/group/extrememathematics/web/another-page-more-surrogate-factoring
It is such beautiful and simple mathematics that it is a shame that there is so much other surrounding this and I freely admit that I came to factoring primarily to force mathematicians to acknowledge my mathematical discoveries.
I found a proof of Fermat's Last Theorem, THE prime counting function, which not only offers a way to disprove the Riemann Hypothesis, but also tells 'why' prime numbers distribute as they do. I've given the definition of mathematical proof. And I cleaned up some areas in logic, explaining how logical form is crucial.
My research is defined like this latest factoring research by its simplicity.
In contrast modern mathematicians have work that is often complex, difficult to understand, and that is a technique to hide the reality that much of it is wrong.
Their research is so abstruse not because mathematics forces it so, but because by making it so, they can hide that it is not correct.
I have come to the sad conclusion that much of that is deliberate.
Because I am someone who breaks their way to make money, modern mathematicians are quite willing to ignore my research and try to continue their scam.
Mathematical research is difficult. It is easier for groups of people to play at being mathematicians than to be real ones. People like me emerge rarely.
But the greatest proof of the lack of real intellectual ability of those in the mathematical community who fight me is that fight.
They can't win. No one has won against someone like me. If they had our world would not be as it is, if Newton had been beaten, or Archimedes, or Einstein.
So factoring is the way to beat them. They will fight still because they're not smart enough to quit and later they will beg the world for mercy.
But remember, they sought to cut the jugular of the world. They sought to end the progress of the human species itself.
They sought to end us all no matter what they claim later.
They tried to make your life meaningless, to take away the future of your children, and to make the sacrifices and efforts of all those who came before us…meaningless.
[A reply to someone who wanted to know more about how James had explained “how logical form is crucial”.]
"Liar's Paradox". I showed how it's about form and is just about a need for a 3 logic, as the "law of the excluded middle" is no law at all.
I think it telling though that modern math people can turn successes like mine into a joke, or claim I do, because they have figured out a style.
Today people think they know what important mathematics looks like, and they think they know how people with correct mathematics should act.
But it's not a big deal now as that's why I went to the factoring problem, where the latest results are just so beautiful and amazing.
IN ways I feel sorry for modern "mathematicians" many of whom were brought into the field after it was corrupted (assuming that really happened in the latter 20th) and taught style as substance and trained to believe that being correct in mathematics is about being believed to be correct by your peers.
It's almost ludicrous to look back at how often these people would call me names or claim that no one believed me as if they had trumped me with the maximum!!!
To think, not being believed, how could I go on? LOL.
Well because most people don't know squat about math and lots of people get even basic things wrong, and, oh yeah, people do lie.
These losers just lie about math. From the proper perspective they just join a long line of people who pretended to be something they are not for personal gain, at the expense of others.
# posted by James Harris @ 01:12 
