The largest known prime number is 2136,279,841 − 1, a number which has 41,024,320 digits when written in base 10. It was found in October 2024 by a computer volunteered by Luke Durant 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. 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 October 2024, the seven largest known primes are Mersenne primes. The last eighteen 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 popularly understood to permit stronger encryption, yet this is incorrect.
Current record
The record is currently held by 2136,279,841 − 1 with 41,024...
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The MILF Messiah
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