Largest known prime number discovered with over 23 million digits

Jonathan Pace, an electrical engineer from Tennessee who has been searching for big primes for 14 years, has discovered the new largest known prime, at over 23 million digits long. Prime numbers are divisible only by themselves and one, like 2, 3, 5, 7, 11, 13 or 17. Euclid proved that there is no largest prime number, and many mathematicians and hobbyists continue to search for large prime numbers. However, the search requires complicated computer software and collaboration as the numbers get increasingly hard to find.

Mr. Pace discovered the new number as part of the Great Internet Mersenne Prime Search (GIMPS), a project started in 1996 to hunt for these massive numbers. GIMPS uses the power of thousands of ordinary computers to search for elusive primes, and the team behind it state that anybody with a reasonably powerful PC can download the necessary software and become a “big prime hunter”.

The number belongs to the Mersenne primes, which are calculated by multiplying together many twos and then subtracting one. The number is the 50th Mersenne prime to be discovered, and the 16th to be discovered by the GIMPS project. It can be computed as 2^77.232.917 – 1 and it has 23.249.425 digits, nearly one million digits longer than the previous record holder, which was identified as part of the same project at the beginning of 2016. The process also relies on thousands of volunteers sifting through millions of non-prime candidates before the lucky individual chances upon their target.

Some important cryptographic algorithms such as RSA critically depend on the fact that prime factorization of large numbers takes a long time. That's one of the reasons for finding larger prime numbers which can be used as cryptographic keys.