Yes, S.T.L: is right, and I believe that more can be done.
No two Mersenne primes can have the same prime divisor, as I recall. So by
listing the composite Mersenne primes (i.e., p is prime but 2^p -1 is not
prime), we can get a list of primes that no longer need to be tried as
divisors of 2^p - 1. So sure, use the +/-1 mod 8 rules, eliminating a
series of trial divisors, and pare the list even more by comparing to known
divisors of Mersenne primes. These prime divisors would presumably be in a
database.
As the work of factoring progresses, one can see that factoring is more and
more important.
If my hypothesis that "No two Mersenne primes can have the same prime
divisor" is incorrect, I appologize in advance.
At 08:30 PM 6/22/99 EDT, you wrote:
><<Now we can filter out multiples of small primes>>
>I'm assuming that we don't need to divide by factors divisible by 3 or 5,
>etc, because a Mersenne number cannot be divisible by 3 or 5 because they
>don't have the structure 2kp+1 themselves? (Excluding the REALLY low Mersenne
>numbers). Ideally, we'd like to only test factors that are prime
>themselves.... Am I right?
>S.T.L.
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