On Jun 15, 8:57=A0am, JSH <jst...@[EMAIL PROTECTED]
> wrote:
> For years I've had a major fear that if I had a major breakthrough
> with integer factorization it might have a very bad, negative impact
> on the global economy but now as I finish out the foundation layer of
> that research it is clear that my research is not impacting the
> world. =A0Yeah, the world is having problems but those are its own.
>
That was then and I still don't see how I'm impacting the world yet,
but my concerns have returned as I've solved the problem of finding
the odd prime p.
> Ok, so what do I mean about the foundation layer?
>
> Well the simplest way to consider what my factoring research does is
> that while mathematicians have traditionally focused on one type of
> congruence I use two:
>
> 1. =A0x^2 =3D y^2 mod S
> 2. =A0z^2 =3D y^2 mod T
>
> where T is your target composite and S is what I call the surrogate,
> and the concept I call surrogate factoring.
>
> A little while back rather than consider S as a whole I started
> focusing on its prime factors, which is why I have a lot of equations
> with
>
> x^2 =3D y^2 mod p
>
> as p is an odd prime factor of S.
A major problem as T increased in size though was, how do you pick p?
The larger the odd prime you used the better, but with larger and
larger primes the odds of picking one that would work dropped.
So I concentrated on using small primes with the Chinese Remainder
Theorem, but there was the issue of false positives (which may or may
not be resolvable as I didn't continue experimental research in that
area).
Now though I think there may be a simpler answer.
> That was a HUGE breakthrough to move from concentrating on S itself,
> where I had control variables I called n, alpha and k, and would
> puzzle over things like what was the way to pick k, to figuring out
> how to get p.
>
> And with the fundamental equations now known that completes the
> foundation layer of surrogate factoring, and removes the need for
> further brainstorming at this point, so there is no need for me to
> discuss further.
>
I'm evaluating the situation this weekend as I ponder what to do
next. It's a t***** problem with a lot of complexity introduced by
the continuing refusal of the mathematical community to acknowledge
this research.
The simplest answer, if possible, may be to develop a working program
and turn it over the United States Government.
I would suggest that mathematicians around the world re-think their
positions on this issue.
My major concern is that I will end up giving up on my dream of
restoring real mathematical research in number theory and leaping
humanity forward mathematically, and instead find myself at the heart
of military endeavors as my problem solving skills are turned instead
to activities that are invisible to the world.
If that happens none of your countries will have any chance of
competing with the US within your lifetimes or the foreseeable future,
and much of what I do will be invisible, but the impact will be
unstoppable.
James Harris
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