Re: Special factorization method sought

From: Unruh (unruh-spam_at_physics.ubc.ca)
Date: 06/29/05 

Date: 29 Jun 2005 18:53:51 GMT

"Pubkeybreaker" <Robert_silverman@raytheon.com> writes:

>"rst 125 digits of the two
>numbers are identical! Not only that, the numbers have the
>same final 125 digits! And the two factors are (probably) prime! "

>Actually, with this much information, I suspect that this number could
>be
>factored by diophantine methods. We know the top 125 digits of each
>factor.
>We do not know the bottom 125, but know that they are identical.

>If you set up the usual simultaneous diophantine system

>(p1 = a0 + a1 *10 + a2*100 + ..., p2 = b0 + b1 * 10 + b2 * 100 +++)
>and
>put p1 p2 = N, with the top 125 values of a and b known, along with
>a0 = b0
>etc. I suspect that we probably could solve this system by lattice
>reduction methods.

Go ahead.