A Mersenne prime is a prime number of the form 2^n - 1. It is known that n must be prime for 2^n - 1 to be a Mersenne prime. 

Currently, the siz largest known prime numbers are all Mersenne primes, mainly because there are fast algorithms for finding them, so they are much easier to search for than other prime numbers. However, it is not known if there are infinitely many Mersenne primes, and only 51 are known currently.

The Euclid-Euler theorem states that there is a one-to-one correspondence between Mersenne primes and even perfect numbers, so this question implies 

. However, they are not equivalent, since it is technically possible for there to be infinitely many odd perfect numbers and only finitely many even ones.