A prime of the form 2^p−1, where p is a prime. The number of known primes of this form is over 50 and keeps increasing as they are discovered by using computers. In 2020, the largest known was 2^82589933−1. Each Mersenne prime gives rise to an even perfect number. It is an open problem whether there are infinitely many Mersenne primes.

http://www.mersenne.org/ Home page of the Great Internet Mersenne Prime Search.