Small Mersenne Prime Factors Prime numbers of the form Mp= 2p − 1 are called Mersenne primes.
For Mp to be prime, p must also be prime.
Any factor q of a Mersenne number 2p − 1 must be of the form 2kp + 1, where integer k
≥ 0. Furthermore, q must be 1 or 7 mod 8.
