The record is currently held by 2 82,589,933 − 1 with 24,862,048 digits, found by GIMPS in December 2018. The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2 k − 1 is simply k ones. The last seventeen record primes were Mersenne primes. As of June 2023, the six largest known primes are Mersenne primes.
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. According to Euclid's theorem there are infinitely many prime numbers, so there is no largest prime. The vertical scale is logarithmic.Ī prime number is a positive integer, excluding 1, with no divisors other than 1 and itself. A 2020 plot of the number of digits in the largest known prime by year, since the electronic computer.
