Mersenne primes are named after a 17th-century French monk and mathematician, Marin Mersenne.

A Mersenne number is a number of the form 2^p - 1, where p is a prime.

A Mersenne prime is a prime number of the form 2^p - 1.

Mersenne Primes.
3 = 2²-1,    7 = 2³-1,    31 = 2⁵-1,    127 = 2⁷-1.
2047 = 2¹¹-1 = 23 x 89 is not a Mersenne prime.