Re: Latest factoring idea, might work

Dave Turner wrote:
> > Re: Latest factoring idea, might work
>
> Looking forward to one that does work

Well, there's a real problem in that I no longer can bring myself to
test my factoring ideas, or it might have all been over months ago.

But with this new idea, it's so much simpler than my previous ones that
it's very tempting to just call it a solution.

The gist of it is easy. With C = p_1 p_2, then the difference of
factors, p_1 - p_2, is enough information to factor C, but when do you
know that difference?

My latest research result will let you find information about it as a
congruence, but I didn't see practical use of that, but then I had an
idea!

Force the difference.

What if you multiply by ab, so you have ap_1 - bp_2 = 1?

Now you've forced the difference, but how do you find ab?

Well, my result lets you find ab mod n_1, where n_1 is some natural you
get to pick, and that may seem small, but by turning the problem
slightly, it looks like a simple way to solving it.

If so, it is easily implementable, and I'm waiting to see if there is
evidence that I am right, and no, as usual now, I refuse to personally
check it with an example.

It's a simple idea, but I have to think it possible that it doesn't
work.

If it does work, then, well, it's a simple idea, easily implemented.

James Harris
Received on Mon May 1 02:06:30 2006