Largest known prime number

The largest known prime number (as of December 2023) is 2^82,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.

A prime number is a natural number greater than 1 with no divisors other than 1 and itself. According to Euclid's theorem there are infinitely many prime numbers, so 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 utilize a specialized primality test that is faster than the general one. As of June 2023, the six largest known primes are Mersenne primes. The last seventeen record primes were Mersenne primes. The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2^k − 1 is simply k ones.

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