My logic might be letting me down here, but since p=M(n) automatically satisfies the first condition of the NMC when M(n) is a Mersenne prime, finding a factor of (2^M(n)+1)/3, as Citrix suggests, would prove that either the double Mersenne MM(n) is composite or the NMC is false. If we didn't already know that MM(n) was composite wouldn't that be progress?
