Re: Factorizaton idea, revisited

From: James Harris (jstevh_at_msn.com)
Date: 04/29/04 

Date: 29 Apr 2004 05:30:04 -0700

"Douglas A. Gwyn" <DAGwyn@null.net> wrote in message news:<sLmdnRBOlrDBCA3dRVn-uQ@comcast.com>...
> James Harris wrote:
> >>>"Gary Shannon" <gary@fiziwig.com> wrote in message news:<6b302915d9081b50c33e6fa9f68c72e3@news.teranews.com>...
> >>>>M = 15645595639 the integer to be factored
> >>>>T = 15645595640 ...
> >>>>T^4 = 59919531205943184213873498032430492160000 ...
> >>>>Now what's the next step?
> >>>You factor T. ...
>
> Sorry, but I'm still wondering what the "j" and "k"
> are supposed to be. Is k a subscript, exponent, or
> factor?

The variables j and k are parameters used in the factorization so they
are neither subscript, exponent, nor factor.

The idea I had was basically to use an asymmetric factorization in the
hopes that I could turn factoring M into factoring some number off M,
like M+1.

The j and k are just pieces of my attempt.
 
> Also, it seems you have replaced the "factor an
> N-digit number" with "factor an N-digit number",
> which on its face doesn't seem like it helps any.
> Is there supposed to be a recursion? If so it
> doesn't seem to converge fast enough.

Not really, if it works (not sure it does) it'd make factoring M a
problem of factoring M+1 or M-1, and if M is odd, you have one factor
off the bat, which is 2. It turns out that you can choose M+1 or M-1,
so you also have 3 as a factor.

So, just like that you would already have 6 as a factor of T, and if
it worked that might be enough by itself to factor M, if the idea
worked.

My motivation in posting was to toss out some ideas that I'm puzzling
over in case someone might have comments on the approach (like maybe
being able to tell me if it will never work!), and I'm not interested
in people thinking it's polished work. It's not.

I'm just musing as it seems to me that it would be neat to shift
factoring some number M to factoring some number off M. But that
doesn't mean it's possible in general to do.

James Harris

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