Sunday, June 15, 2008


JSH: Diminishing concerns on factoring

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.

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.

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.

Succinctly, the basic research phase on the primary layer is complete.

World seems ok, as my worst fears haven't realized, so I'm kicking back, relaxing and moving to other problems as a MAJOR issue right now is monetization of the web, or so-called Web 2.0 as it's coming up as a bigger and bigger problem to get revenue flowing for creative people around the world, and my current focus is on the biggest player, so YouTube is the focus of problem solving efforts and that will take up most of my time indefinitely.

Math research is done for this iteration.

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