 Mersenne prime

A Mersenne prime is a Mersenne number that is a prime number. It is the prime factor required by the Euclid-Euler theorem; $3,7,31,127$ generate $6,28,496,8128$. The family is named after Marin Mersenne.

A Mersenne prime is a specific type of prime number that can be expressed in the form \(M_n = 2^n - 1\), where \(n\) is a positive integer. In other words, if \(M_n\) is prime, then \(n\) itself must also be prime.