The world's largest known prime number has been discovered, but we can't show it because it's so large it would take up 21 standard-sized novels to turn into text. Called M136279841, its shorthand version is 2136,279,841-1. That comes to 41,024,320 digits.
If you remember your math lessons from school, a prime number is any number that can only be evenly divided by itself or 1. It's one of the most basic concepts in mathematics and how they work has produced some of the most profound questions in the field, such as is there a pattern inside prime numbers? How are they distributed? What about the sum of two primes, or primes that form palindromes that read the same forward and backwards?
If this seems too esoteric, prime numbers are used every time someone uses the internet. Modern encryption techniques are based on equations with two solutions, each of which produces a prime number – one that can be used to encrypt data and the other to decrypt it.
The new largest prime number was discovered by Luke Durant of San Jose, California, who is an amateur researcher and former NVIDIA employee, on October 11, 2024 and confirmed by independent computation on October 12. However, Durant didn't use a pencil and paper – a lot of paper, like 11,000 sheets just to write out the results, which fill up a 39.9 MB text file.
Instead, he was one of a number of volunteers who have downloaded free software to do the number crunching as part of the Great Internet Mersenne Prime Search (GIMPS) that's been running since 1996. Today, the search is essentially a giant cloud supercomputer that is based on thousands of server GPUs, spanning 24 data center regions over 17 countries.
GPUs are an important key to the search because these graphic processors have proven to be extremely good at dealing with more than digital images. In recent years, they've become key to Large Language Model AIs and for the complex calculations involving prime numbers. In this case, it's a class called Mersenne primes, which can be expressed by the formula Mn = 2n-1, where M is the prime number and n is an integer. These have been central to number theory since the days of Euclid in Ancient Greece.
According to the GIMP organization, the new prime is 16 million digits larger than the previous record prime number and the 52nd known Mersenne prime ever discovered. As the primes become larger, they become increasingly difficult to find. The new record holder was found on an NVIDIA A100 GPU server running in Dublin, Ireland and confirmed in San Antonio, Texas, netting Durant a prize of US$3,000, which he is donating to charity.
Source: GIMPS
