----- Original Message ----- From: "Alexander Kruppa" <[EMAIL PROTECTED]> To: "Daran" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Monday, December 10, 2001 12:16 AM Subject: Re: Mersenne: P-1 Stage 2
> P-1 stage 1 computes x = a^E (mod N), where E is the product of all > primes and prime powers <= B1. Right. The math page says 3^(2*E*P) and neglects to mention the (mod N). It also doesn't make it clear that E is a product of prime *powers*, and not just a primordial. I didn't understand how that could work, but this makes rather more sense. So if we were using P-1 to factorise 1000 using B1=15 we would calculate E = 2^9 * 3^6 * 5^4 * 7^3 * 11^2 * 13^2 Or did you mean E = 2^3 * 3^2 * 5 * 7 * 11 * 13 ? [...] > For each x^p_i we compute this way, we multiply this x^p_i-1 to an > accumulator. (Mod N) ? This generalises surely. You could have a third bound B3, and allow one prime between B1 & B2, and a second prime between B1 & B3. And then a fourth bound B4 and so on. (I'm not suggesting that it would be useful to implement this.) Thanks for a full and thought-provoking reply. > Alex Daran G. _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
