I've been wondering about this lately... If we are to begin P-1 testing on larger exponents, this implies lower trial factoring limits (though possibly only by 1 or 2 bits). Now, P-1 requires an investment of a GCD on two numbers each of similar size to Mn. So, since we are investing this much (computational) engery in a GCD, why not cram in as many factors as we can? Would it be possible to find multiply the (a^q-1) mod Mn by small (possible) factors skipped due to the lower factoring bounds faster than it would to directly check these possible factors? Gack, that was a bit unclear, say that k*n+1 divides Mn, k is non-B1-smooth. Which would take more time, checking (directly) to see if k*n+1 divides Mn, or multiplying (a^q-1) by k*n+1? (assuming k*n+1 is around 64 bits) Lucas _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
