2^p - 1 can only be prime (a so-called Mersenne prime) if p is prime. 2^8 - 1 thus cannot be a prime, since 8 is composite. (Note that is it not _sufficient_ t

2^p - 1 can only be prime (a so-called Mersenne prime) if p is prime. 2^8 - 1 thus cannot be a prime, since 8 is composite. (Note that is it not _sufficient_ that p is prime, but it is necessary.)