JSH: Factoring, number theory

jstevh_at_msn.com
Date: 02/13/05 

Date: 13 Feb 2005 10:33:40 -0800

So now with the easy proof, there's not an issue of whether or not
surrogate factoring must work.

Now there's also the theoretical side to think out some more.

Like clearly then for *any* natural number T, since you have a finite
set of natural numbers n and m, such that n^2 - m^2 = T, then there is
some relationship between the prime factors of T, and the prime factors
of n and m of each pair.

That's not terribly surprising in retrospect because it's a finite set.

And the proof of the connection is trivially easy.

So for any natural number T, there is this finite set, and a mapping
between the prime factors of any natural n and m such that n^2 - m^2 =
T.

One thing is clear, no one thought to generalize out a bit, or the
factoring problem would not have been considered such a difficult one.

It only took *two* quadratics while most factoring is based on ideas
from one quadratic.

If even just pairs of quadratics had been played with before, the
solution I found would have been known before.

There are serious implications for Internet security. I don't know
exactly what to do next.

James Harris

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