Mersenne Prime

Mersenne Primes are numbers that can be expressed in the form  2p − 1, where p is a prime number. Not all numbers of the form 2p − 1 are prime, but those which are prime are known as Mersenne primes, named after French mathematician, Marin Mersenne. Numbers of the form 2n − 1 where n is composite cannot be prime.
Since 1992, when 2756,839 − 1 was proved prime, the largest known prime number has always been a Mersenne Prime. In 2014,  257,885,161 − 1 was found to be prime, which contains 17,425,170 digits. As of 2022, the largest known prime is 282,589,933 -1 which has 24,862,048 digits.
Mersenne Primes are closely linked with Perfect numbers (numbers which are the sum of their proper divisors). For any Mersenne Prime, 2p - 1, the composite number (2p-1)x2p-1 is perfect.
==The First Few Mersenne Prime Numbers==
3.png|link=3|22 - 1
7.png|link=7|23 - 1
31.png|link=31|25 - 1
127.png|link=127|27 - 1
8191.png|link=8,191|213-1
131071.png|link=131,071|217 - 1
524287.png|link=524,287|219 - 1
File:2147483647.webp|2^31 - 1
==See also==
Double Mersenne Prime
Category:Types of Primes
Category:Mersenne Primes