Thread: 2.2 million?
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Old 2003-02-22, 08:42   #5
Oct 2002

43 Posts
Default Re: largest non-mersenne

Originally Posted by TTn
PS I notice k is seldomly prime, for Riesel primes.
Does anyone know the mechanism for this?
If p divides k, then p does not divide k*2^n-1. This means that N=k*2^n-1 is prime with probability k/phi(k) * 1/ln(N) instead of probability 1/ln(N).

For k<100 with k*2^n-1 prime, this moves the probability that k is prime from 1 in 4 to 1 in 7; for k<1000, the probability of k prime moves from 1 in 6 to 1 in 11; for k<10000, the probability moves from 1 in 8 to 1 in 16.
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