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.
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