Re: JSH: Diminishing concerns on factoring

On Jun 15, 8:57 am, JSH <jst...@xxxxxxxxx> 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. Yeah, 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. x^2 = y^2 mod S
2. z^2 = 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 = 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 thorny 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.


WTF? I take it that you now deem the only one worthy of
replying to your articles, is ... you. Get help, Mr.
Harris.

Tom


James Harris
.

Relevant Pages

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  • Re: Amateur math, neat relation
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