Mersenne number

Definition

For a natural number $n$, the $n$-th Mersenne number is $M_n = 2^n - 1$.

Remarks

The first values are $M_1 = 1$, $M_2 = 3$, $M_3 = 7$, $M_4 = 15$ and $M_5 = 31$. In binary, $M_n$ is written with $n$ digits $1$. Some texts call $M_n$ a Mersenne number only when $n$ is prime. A Mersenne number that is prime is a Mersenne prime.

Explanations

L1 human

A Mersenne number is one less than a power of $2$. For example, $2^{10} - 1 = 1023$, which is $1111111111$ in binary.