The largest known prime number is 2136,279,841 − 1, a number which 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 to the Great Internet Mersenne Prime Search (GIMPS).[1]
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[update], the seven largest known primes are Mersenne primes.[2] The last eighteen record primes were Mersenne primes.[3][4] The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2k − 1 is simply k ones.[5]
Finding larger prime numbers is sometimes presented as a means to stronger encryption, but this is not the case.[6][7]
- ^ "GIMPS Project Discovers Largest Known Prime Number: 2136,279,841-1". Mersenne Research, Inc. 21 October 2024. Retrieved 21 October 2024.
- ^ "The largest known primes – Database Search Output". Prime Pages. Retrieved 19 March 2023.
- ^ Caldwell, Chris. "The Largest Known Prime by Year: A Brief History". Prime Pages. Retrieved 19 March 2023.
- ^ The last non-Mersenne to be the largest known prime, was 391,581 ⋅ 2216,193 − 1; see also The Largest Known Prime by year: A Brief History originally by Caldwell.
- ^ "Perfect Numbers". Penn State University. Retrieved 6 October 2019.
An interesting side note is about the binary representations of those numbers...
- ^ McKinnon, Mika (January 4, 2018). "This Is the Largest Known Prime Number Yet". Smithsonian. Retrieved July 6, 2024.
- ^ Johnston, Nathaniel (September 11, 2009). "No, Primes with Millions of Digits Are Not Useful for Cryptography". njohnston.ca. Retrieved July 6, 2024.