Mersenne prime

A Mersenne number is a positive integer that is one less than a power of 2.

M_n = 2ⁿ − 1

The Mersenne numbers consist of all 1s in base-2. The first few Mersenne numbers are 1, 3, 7, 15, 31, 63, 127, 255, ... , corresponding to 1, 11, 111, 1111, 11111... in binary.

A Mersenne prime is a Mersenne number that is prime. Read more here.