Largest known prime number

The largest known prime number as of June 2026 is 2136,279,841 − 1, a number that has 41,024,320 digits when written in the decimal system. It was found on October 12, 2024, on a cloud-based virtual machine volunteered by Luke Durant, a researcher from San Jose, California, to the Great Internet Mersenne Prime Search (GIMPS).

A prime number is a natural number greater than 1 with no divisors other than 1 and itself. Euclid's theorem proves that for any given prime number, there will always be a higher one, and thus there are infinitely many; there is no largest prime.

Many of the largest known primes are Mersenne primes, numbers that are one less than a power of two, because they can be verified by a specialized primality test that is faster than the general one. As of October 2024, the seven largest known primes are Mersenne primes. The last 18 record primes were Mersenne primes. The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2k − 1 is simply k ones.

Finding larger prime numbers is sometimes presented as a means to stronger encryption, but this is not true. While large primes with hundreds of digits are indeed used for cryptography, primes with millions of digits are not.

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