Definition:Mersenne Number

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

The number $2^p - 1$, in this context, can be denoted $M_p$.

Also see

 * Factors of Mersenne Numbers, where it is shown that that all divisors of $2^p - 1$ are of the form $2 k p + 1$.


 * Thus any factors of Mersenne numbers can conveniently be referred to by the value of $k$.


 * Definition:Mersenne Prime
 * Lucas-Lehmer Test