Generate Mersenne numbers, flag Mersenne primes, look up a term, or test whether a number is one less than a power of two.
A Mersenne number is M(n) = 2n − 1. The exponent n is the natural
index here, and the list runs from n = 1 upward. A Mersenne prime is a Mersenne
number that is itself prime, which requires n to be prime as well.
Early values: M(1) = 1, M(2) = 3, M(3) = 7, M(4) = 15, M(5) = 31. Of those, 3, 7, and 31 are Mersenne primes.