Mersenne number

Definition
For any natural number $$n$$, the $$n^{th}$$ Mersenne number, denoted $$M_n$$, is defined as:

$$M_n = 2^n - 1$$

If $$M_n$$ is prime, it is termed a Mersenne prime. A necessary (but not sufficient) condition for $$M_n$$ to be prime is that $$n$$ itself be prime.