Alexey
> Ok, George's programs looks for only for factors of M(n) in form
>1) 2kn+1
> that's clear why
>2) 1,7,17,23,31,41,47,49,71,73,79,89,97,103,113,or 119 modulo 120
> but this is not. Why factors 120k+13 are not considered? Or 120k+19? Why
only those 16 reminders of
>~30 primes below 120?
This follows from point 1, if q=2kp+1 divides 2^p-1, then it divides 2^kp-1
as well, ie 2^(q-1)/2-1. In other words, 2 is a quadratic residue mod q, so
q is of the form 8n+1 or 8n+7. This, plus the conditions that q is not
divisible by 3 or 5, gives precisely the 16 values mod 120 that you see in
prime95.
Chris Nash
Lexington KY
UNITED STATES
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Co-discoverer of the 9th largest known prime: 302442855.2^336211+1
