Mersenne primes

Mersenne primes are a special class of prime numbers that can be expressed in the form \( M_n = 2^n - 1 \), where \( n \) is a positive integer. For a number of this form to be classified as a Mersenne prime, \( n \) itself must also be a prime number. The reason for this restriction is that if \( n \) is composite (i.e.