>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.
I don't think this would be very effective for the simple reason that it would
take longer to read from disk than it would to just check the factor.
>These prime divisors would presumably be in a database.
It is possible to do this using methods like Chris Nash's PriMers method.
In this, you calculate all the prime numbers ==+/-1 mod 8 up to a certain
point. Then you can factor that prime-1, and test the mersenne exponents that
are factors.
-Lucas Wiman
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