> From: Jiho Kim
> Subject: Mersenne: Rather naive question
>
> 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.
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.
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