Re: Mersenne: Simple question about P-1 factoring method

1999-08-17 Thread Peter-Lawrence . Montgomery
Will Edgingtom writes: If I understand P-1 factoring correctly, then using it to a stage one bound of k to try to factor M(p) will find all possible factors less than or equal to 2*k*p + 1. I'm assuming that p is less than k (or p is always used in the powering) and the convention several

Re: Mersenne: Simple question about P-1 factoring method

1999-08-17 Thread Will Edgington
[EMAIL PROTECTED] writes: Am I correct? Or could a factor smaller than 2*k*p + 1 be missed in some cases? In the last example a factor 16*97 + 1 could be missed. Otherwise all factors below 2*k*p + 1 should be found. One extra squaring will achieve the 2*k*p + 1 bound.

Re: Mersenne: Simple question about P-1 factoring method

1999-08-17 Thread Lucas Wiman
If I understand P-1 factoring correctly, then using it to a stage one bound of k to try to factor M(p) will find all possible factors less than or equal to 2*k*p + 1. Yes, of the form n*p+1 (not 2*n*p+1 :). This is for the simple reason that every power of a prime =k must divide Q (due to