Mersenne Prime

A Mersenne prime is a prime number that is one less than a power of two, written 2 to the n minus 1 for some whole number n. They are named after the French friar Marin Mersenne, who studied numbers of this form in the early seventeenth century. A number of this form can only be prime if its exponent n is itself prime, though a prime exponent does not guarantee the result is prime. As of 2024, 52 Mersenne primes are known, the largest being 2 to the 136,279,841 minus 1, found in October 2024, and since 1997 essentially every new one has been discovered by the distributed computing project GIMPS, the Great Internet Mersenne Prime Search. The Euclid-Euler theorem ties Mersenne primes directly to even perfect numbers: every Mersenne prime generates an even perfect number, and every even perfect number arises this way.