Mersenne primes are a category of numbers studied by the monk Marin Mersenne (1588-1648) and by Pierre de Fermat (1601-1665), and defined by: Mq = 2q - 1 where q is a prime number.
Every Mersenne prime can be used to construct an even perfect number 2q-1 Mq , equal to the sum of its divisors (example: 6 = 21(22-1) = 1+2+3).
It is possible to prove that a Mersenne prime is indeed prime by a test invented by Edouard Lucas (1842-1891) and rigorously proved by Derrick Lehmer (1905-1991): the LLT test (Lucas-Lehmer-Test).
This test consists in calculating the elements of the series: Si+1 = Si2 - 2 (mod Mq), starting from S0 = 4 . if Sq-2 = 0 (mod Mq) , then Mq is prime.