>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.
This is not quite right. The primes must be ==3 mod 4. For example,
29 is prime and ==1 mod 4, but 59 does not divide 2^29-1.
I'm not sure whether or not it has been proven whether or not there are
an infinity of Sophie Germain primes of the form 4*n+3. I imagine there
would be, as there are an infinity of primes in the form 4*n+1 and 4*n+3.
-Lucas Wiman
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