It occurs to me that some of you may not understand how my research
changes the landscape with factoring so I want to explain simply and
give some factoring basics.
First off, if you have z^2 = y^2 + nT
where T is your target to factor, and you also have z mod p_1, z mod
p_2, and z mod p_3, where z is for a non-trivial factorization and
those are odd primes with a minimum value greater than 2sqrt(nT)/3,
then necessarily you can calculate z exactly and with z you can factor
nT from
(z-y)(z+y) = nT.
That is just an absolute in terms of basic algebra.
So it IS a big deal for me to present equations that allow you to just
calculate z mod p.
Most modern factoring methods in some way or another use an equation
like z^2 = y^2 + nT, or more familiarly you often have x^2 = y^2 mod
N, where N is the target composite, so it's just about variable names
and if you know any math at all you know that ****fting letters is not
a big deal.
Even the Number Field Sieve is a lot about using x^2 = y^2 mod N, as
in trying to find x and y (I think it uses two congruences of that
type), so the result I have has implications for the most advanced
factoring techniques known.
But, you may then naturally wonder, if it's such a big deal to find z
mod p, then how can it be something argued out on newsgroups without
experts in the field caring?
One simple possible answer to that question is that I must be wrong.
REMEMBER, if p_1, p_2 and p_3 can be found in the size range necessary
then it is an ABSOLUTE that you can factor non-trivially.
I claim to have a method that gives z mod p, so if that claim is
correct and you can get z mod p in the necessary range for just three
prime numbers then ABSOLUTELY you will factor non-trivially.
So theory says one thing, absolutely. Where notice I still haven't
answered the question of whether or not I must be wrong.
Well, there's the derivation which you can look over, and there is
doing examples and you might wonder if maybe with a big target
composite T, maybe it IS really hard to find odd primes p that will
work, and you can muddle along with those questions believing there
must be something wrong somewhere or top people in the field would
acknowledge this result!
I think this situation for some of you is a test of your trust in
people versus your trust in mathematics and it's probably not fair,
but I think some of you wrongly believe that you have mathematical
ability, when you do not.
Short of it is that how the newsgroups react doesn't matter. No
matter what if the research is viable that will be known and probably
in a rather short amount of time as we have a world today that
consumes information. But what you cannot forget later, or I don't
want you to forget it, is if you couldn't resolve the issue on your
own despite the algebra being easy and the problem being hugely
significant.
As if you cannot evaluate easy algebra and get the right answer when
it's handed to you because you're waiting on some other people or
trusting that someone else out there has the judgment you need, then
you are NOT a mathematician, no matter what you tell yourself when you
look in the mirror.
You are then a social person who relies on other people who really do
know mathematics to tell you what is true or not.
James Harris
|
