Largest known prime number discovered by amateur mathematician

A number with more than 40 million digits has been discovered to be the largest known prime number by a network of amateurs.

The number is 2^136279841-1. It has 41,024,320 digits. It was found by 36-year-old researcher and former NVIDIA employee Luke Durant on 12 October. The number was tested on other computers using different programs and confirmed prime on 19 October.

Prime numbers are wholly divisible by only 1 and themselves. For example, 7 is prime because only 1 and 7 go into 7 without leaving a remainder.

Primes have been an area of interest for mathematicians for centuries.

Among the most famous studiers of prime numbers is French monk Marin Mersenne (1588–1648 CE).

Mersenne is most well-known today for his attempts to find a formula that would represent all primes. He was ultimately unsuccessful in this quest, but Mersenne primes are still found today using a simple formula that he put forward in 1644: 2^p-1 is a prime number if p is a prime number.

No one has found a better method for finding more prime numbers than Mersenne.

But, as the power of 2 increases, so does the computing power to both calculate the possible Mersenne prime, and then to confirm whether it is a prime or composite number.

The new number, dubbed M136279841 rather than its full value for obvious reasons, is the 52nd Mersenne prime to be discovered.

Its finder, Durant, is a member of the Great Internet Mersenne Prime Search (GIMPS) – a collective of volunteers founded in 1996 that uses free software to hunt for Mersenne primes.

GIMPS has successfully found the last 18 Mersenne primes.

Durant’s number trumps the previous largest Mersenne prime, found by GIMPS in 2018, by 16 million digits.

A statement by GIMPS announcing the discovery notes that the 52nd prime is the first to be found on something other than an ordinary PC. Durant’s find relied on GPUs – previously used primarily for video cards to power gaming PCs, but now sparking an increase of power which is also being used in the development and use of artificial intelligence algorithms.

As with other GIMPS Mersenne prime discoverers, Durant has been awarded a US$3,000 (A$4,530) prize which he says he will donate to the Alabama School of Math and Science’s maths department.

Correction: 5/12/24: A previous version of this story had an incorrect name for the number: M136279821 rather than M136279841. The mistake was made during transcription.