At 10:47 AM 7/6/99 +0200, Benny.VanHoudt wrote:
>Now lets only focus on the set 2^p - 1 with p prime, i.e., the set
>of numbers that we are checking out at GIMPS. Has anyone proven that
>an infinite number these are NOT prime (this is VERY likely to be
>true)? If so, how can one prove this easily (it is probably not
>possible to indentify a subset that is NOT prime as above
>because then we would not consider all of them for GIMPS)?
>
If 2p+1 is prime then it divides 2^p-1. If it has been proven that there are
in infinite number of prime pairs p and 2p+1 then this proves that there are an
infinite number of 2^p-1 that is not prime when p is prime. These are called
Sophie Germain primes, and it has been proven that there are an infinite number
of them, therefore there are an infinite number of composites of the form 2^p-1
when p is prime.
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| Jud "program first and think later" McCranie |
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