- First of all please let me apologise for my p.2^p+1 is never prime for p
prime failed proof. A re-examination clearly demonstrated the logical flaw.
However, I set about the puzzle with renewed vigour, and have discovered
that if (p,p+2) are twin primes then p+2 divides p.2^p+1. Here goes:
p.2^p+1 = (p+2).2^p - [ 2^(p+1) - 1]
If p+2 is a prime, then p+1 = p+2-1, hence 2^(p+1)-1 = 2^((p+2)-1)-1 ==