>> How exactly are the exponents to be tested chosen? It must be prime, of
>> course, and so do we just test all prime exponents? Or is there a further
>> effort that GIMPS makes to weed out mersenne composites with prime
>> exponents?
>
>Good question. Primenet itself gets an allocation of exponents to check out
>every time Scott and George do a database synchronization. To my knowledge,
>George keeps the best track of what exponents have and have not been tested
>as part of the GIMPS project. I'm not sure how many other non-GIMPS folks
>are doing testing, but I'd hope that they work with George on who is testing
>what exponents.
Or, at least, reports the results to George.
>
>As for weeding out, basically it's just the trial-factoring. Each exponent
>is trial-factored up to a certain bit size (based on the size of the
>exponent) to eliminate (relatively) small factors. If a factor is found,
>it's obviously not tested with the LL test.
>
>Other than that, they all have to be looked at.
I think it's been pointed out before that exponents which are Sophie Germain
primes can't possibly give rise to a Mersenne prime. However they are bound
to have a small factor, so it's not worth doing an explicit test for Sophie
Germain'ness.
Regards
Brian Beesley
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