> >For now, it looks to me like GIMPS is the most reliable way of looking
> >for primes. Does anyone on the list have a view on this?
>
> Both are quite reliable methods for finding primes. One is good at
> finding good sized primes, the other good at finding record primes.
> BTW, the Proth program and OpenPFGW program could be used to find
> world-record primes. They are less than half as efficient as prime95 -
> but you get to test numbers that are much smaller than the M12000000
> currently being assigned by Primenet.
The best candidates are not the numbers of the form k.2^n+/-1 but the
numbers of the form b^(2^n)+1 (Generalized Fermat Numbers). Like for
Mersenne numbers, we can use a DWT which computes directly x^2 (mod b^N+1).
Then if we select carefully the ranges for b, the computation time to test
the probable primality of a GFN is the same than the test of a Mersenne
number with the Lucas-Lehmer test.
The current version of Proth.exe implements this algorithm: I ran a bench on
a PIII 600 and it is as fast as Prime95 up to about 10^6 digits and is about
30% slower for 12,000,000 digits.
An operation with a GFN of 3,000,000 digits is about 4 times faster than an
operation with a Mersenne number of 12,000,000 digits and the number of
operations to compute to test a number 4 times smaller is divided by 4. And
smaller is the number, larger is the probability to find a prime.
Yves
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