What Is a Mersenne Prime?

A Mersenne prime is a prime number of the form 2^p − 1, named for the 17th-century French friar Marin Mersenne, who studied them. Not every value of p gives a prime — 2¹¹ − 1 = 2047 = 23 × 89, for instance — but when it does work out, the result has a special structure that makes it unusually easy to test for primality compared to an arbitrary number of the same size, even though finding candidates in the first place is still a massive computation.

Why they’re the biggest known primes

The Lucas–Lehmer test, a primality test specific to numbers of the form 2^p − 1, is dramatically faster than general-purpose primality testing. That’s the entire reason essentially every record for “largest known prime” for the last several decades has been a Mersenne prime — it’s not that they’re more common, it’s that they’re the only scale at which testing a specific candidate is remotely feasible.

GIMPS

Since 1996, the search has been run largely by the Great Internet Mersenne Prime Search (GIMPS), a volunteer distributed-computing project: anyone can download the software and donate spare compute time to testing candidate exponents. The current record, 2^136,279,841 − 1 — a number with just over 41 million decimal digits — was found in October 2024 by GIMPS volunteer Luke Durant, using a GPU-based compute cluster spanning roughly two dozen data centers, ending a 28-year run of CPU-based discoveries.

What’s in the Registry today

The Registry’s Mersenne prime records currently cover the historical catalog up through 2¹³²⁰⁴⁹ − 1 — the record does not yet include Durant’s 2024 discovery or any exponent found since. Each record is exact and proven, not estimated: a Mersenne prime is either verified or it isn’t, with no partial credit, which makes this one of the cleanest categories in the entire Registry to keep accurate.

Why they’re here

A “largest known prime” claim is a specific, checkable assertion, not a matter of opinion — and that’s exactly the kind of claim this Registry is built to track precisely, with the exponent, the discoverer, and the verification method attached to the record rather than repeated from memory.