On 6 Jul 99, at 11:22, Jud McCranie wrote:
> If 2p+1 is prime then it divides 2^p-1.
Only if p (and therefore 2p+1 also) are congruent to 3 (modulo 4).
> 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.
True...
> These are called
> Sophie Germain primes, and it has been proven that there are an infinite number
> of them,
Can you please supply a reference to this proof? Chris Caldwell's
Prime Pages show this as a conjecture (with a strong heuristic
argument).
See http://www.utm.edu/research/primes/lists/top20/SophieGermain.html
In any case, proving that there an infinite number of S-G primes
congruent to 3 (modulo 4) is, presumably, a bit harder - though it
would seem very likely to be true - possibly a bit _less_ likely than
there being only a finite number of composite Mersenne numbers with
prime exponents, though!
Regards
Brian Beesley
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