What are Mersenne Primes?
A Mersenne prime is a prime number that is one less than a power of two. They have the form:
For $M_p$ to be prime, the exponent $p$ must itself be prime (though not all prime exponents yield Mersenne primes).
All 51 Known Mersenne Primes
There are currently only 51 known Mersenne Primes. The exponent $p$ for each is:
2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657, 37156667, 42643801, 43112609, 57885161, 74207281, 77232917, 82589933, 136279841
The Latest Discovery
The last number in the list, 136279841, was discovered in 2024 by the Great Internet Mersenne Prime Search (GIMPS). At 41,024,320 digits, it eclipses by more than 16 million digits the previous largest known prime number found by GIMPS nearly 6 years earlier.
Note: There is no code block for generating Mersenne Primes because they are incredibly hard to find. Use the Lucas-Lehmer test to verify them instead.
Related Resources
GIMPS - Great Internet Mersenne Prime Search
Join the distributed computing project that discovered the largest known primes.
Download the Largest Known Prime
All 41,024,320 digits of the 51st Mersenne prime.
Lucas-Lehmer Test
C++ code to verify if a number is a Mersenne prime.
Previous Record (2018)
The 50th Mersenne prime discovery announcement.