Wednesday, February 28, 2007
JSH: Good news!
Rather than just talk about my latest surrogate factoring idea and worry about consequences I've been playing with it, using small primes, and it works.
x^2 = y^2 mod T
and
k^2 = 2xk mod T
define a simple family of relations that allow you to factor a target composite T, by instead factoring some other number that I call the surrogate. The smart ones among you know just by looking that with all integers, for any integer k there must exist x and y mod T.
That means this remarkably simple idea has to work mod T, so once you pick a k, all you can do is move things around in multiples of T, as you look for non-trivial factorizations.
For the more brilliant among you, the surest test of this idea is asking, how could I find solutions for x and y using k, if I already knew the factorization of T?
That's one of the things I puzzled over for months as I considered this idea from a distance, and mostly worked on theory.
Oh yeah, for those of you who wondered, no, there is no way that mathematicians of the world could NOT have some clue that a lot of what they were doing was bogus when they are clearly trying their very best to sit quietly on this information, hoping nothing will happen.
As, hey!!! A person can't invent a new way to factor and it not get noticed.
Even back in the 1800's this would have been buzzing around the world.
So now there is no doubt—supposedly top mathematicians around the world MUST have known on some level that what they were doing was bogus.
Like, imagine if say, Andrew Wiles were serious about desperately wanting a real answer for Fermat's Last Theorem and really believed he'd found one, if there were a hint of a clue that he was wrong, would he hide from it? Or would he chase it down to be sure?
What if instead he and his colleagues just tried to deny, until brought down by brilliant research in another area, where they still at first tried to deny?
Could anyone doubt that they were cons all along?
It is EASY to lie about mathematics. It is a magnet for cons.
The real math is done by the people who work in practical areas, doing things like building better cars, faster computer chips, and better plastics. The "pure math" people are mostly not doing anything at all, and at this late stage in the game, they are completely controlled by con artists who know how to play at being real mathematicians though they do no important research at all…
And so many of you were so easily conned, by people who now have to sit still, hoping against hope, that the world ignores brilliant new knowledge to its own detriment, or they are found out...
A reply to someone who wrote that the values of X and Y in the examples do not satisfy the congruence, and so the presence of factors of T in X+Y or X-Y are due to something else.
Read the theory carefully. Mathematically you can do most of that theory with a prime factor p of T, and the smaller the k, that is, the lower the k/T ratio, the more you squeeze out the larger factors.
x^2 = y^2 mod p
and
k^2 = 2xk mod p
will do just fine to non-trivially factor.
I use small k's because it's easier for me to factor them.
With surrogates that are fully factored and the small numbers currently being used, it is factoring somewhere between 50% and 33% of the time, which is of course not random.
It is not random. If you test it properly then it is clearly not random.
People claiming otherwise either are screw-ups or liars.
I'm pushing people more towards my math blog and Extreme Mathematics group now, where I have started putting up examples.
The best overview on the planet of surrogate factoring is probably at my group:
http://groups.google.com/group/extrememathematics/web/surrogate-factoring
Kind of wild, I guess, and it is cool having invented my own factoring method.
It may be key to ending the Math Wars.
And finally, the world will finally know that they were fought, how they were fought, and why…
x^2 = y^2 mod T
and
k^2 = 2xk mod T
define a simple family of relations that allow you to factor a target composite T, by instead factoring some other number that I call the surrogate. The smart ones among you know just by looking that with all integers, for any integer k there must exist x and y mod T.
That means this remarkably simple idea has to work mod T, so once you pick a k, all you can do is move things around in multiples of T, as you look for non-trivial factorizations.
For the more brilliant among you, the surest test of this idea is asking, how could I find solutions for x and y using k, if I already knew the factorization of T?
That's one of the things I puzzled over for months as I considered this idea from a distance, and mostly worked on theory.
Oh yeah, for those of you who wondered, no, there is no way that mathematicians of the world could NOT have some clue that a lot of what they were doing was bogus when they are clearly trying their very best to sit quietly on this information, hoping nothing will happen.
As, hey!!! A person can't invent a new way to factor and it not get noticed.
Even back in the 1800's this would have been buzzing around the world.
So now there is no doubt—supposedly top mathematicians around the world MUST have known on some level that what they were doing was bogus.
Like, imagine if say, Andrew Wiles were serious about desperately wanting a real answer for Fermat's Last Theorem and really believed he'd found one, if there were a hint of a clue that he was wrong, would he hide from it? Or would he chase it down to be sure?
What if instead he and his colleagues just tried to deny, until brought down by brilliant research in another area, where they still at first tried to deny?
Could anyone doubt that they were cons all along?
It is EASY to lie about mathematics. It is a magnet for cons.
The real math is done by the people who work in practical areas, doing things like building better cars, faster computer chips, and better plastics. The "pure math" people are mostly not doing anything at all, and at this late stage in the game, they are completely controlled by con artists who know how to play at being real mathematicians though they do no important research at all…
And so many of you were so easily conned, by people who now have to sit still, hoping against hope, that the world ignores brilliant new knowledge to its own detriment, or they are found out...
A reply to someone who wrote that the values of X and Y in the examples do not satisfy the congruence, and so the presence of factors of T in X+Y or X-Y are due to something else.
Read the theory carefully. Mathematically you can do most of that theory with a prime factor p of T, and the smaller the k, that is, the lower the k/T ratio, the more you squeeze out the larger factors.
x^2 = y^2 mod p
and
k^2 = 2xk mod p
will do just fine to non-trivially factor.
I use small k's because it's easier for me to factor them.
With surrogates that are fully factored and the small numbers currently being used, it is factoring somewhere between 50% and 33% of the time, which is of course not random.
It is not random. If you test it properly then it is clearly not random.
People claiming otherwise either are screw-ups or liars.
I'm pushing people more towards my math blog and Extreme Mathematics group now, where I have started putting up examples.
The best overview on the planet of surrogate factoring is probably at my group:
http://groups.google.com/group/extrememathematics/web/surrogate-factoring
Kind of wild, I guess, and it is cool having invented my own factoring method.
It may be key to ending the Math Wars.
And finally, the world will finally know that they were fought, how they were fought, and why…
# posted by James Harris @ 23:19 
