Amateur Mathematician Discovers the Largest Known Prime Number, With More Than 41 Million Digits

In the 17th century, French monk and mathematician Marin Mersenne developed a method to find prime numbers: values that are only divisible by themselves and one. Some examples include two, three, five and seven, and while there are technically an infinite amount of prime numbers, they get significantly harder to identify as they grow larger.

Mersenne’s simple method, which is one of many devised to find primes, is subtracting one from powers of two. For example, the prime number three is two squared, minus one. Seven is two cubed, minus one. Not all prime numbers work out that way, but the rare ones that do are called Mersenne primes.

Now, Luke Durant, a 36-year-old researcher and former employee of tech giant NVIDIA, has discovered the 52nd Mersenne prime, which also happens to be the largest prime number known to mathematicians: 2^136,279,841 minus one. This goliath number, dubbed M136279841, has 41,024,320 decimal digits. The feat, which beats out the previous record by 16 million digits, was announced in a statement by the Great Internet Mersenne Prime Search (GIMPS) on Monday.

GIMPS is a collective of volunteers that use free software to hunt for Mersenne primes. Since its founding in 1996, the group has discovered the last 18 Mersenne primes, with a $3,000 prize awarded to each lucky volunteer that has identified one. Since joining GIMPS in October 2023, Durant has become its “most prolific contributor,” per the statement.

To find M136279841, Durant used the GIMPS software and a supercomputer made up of thousands of graphics processing units (GPUs) that were spread across 24 data centers in 17 countries. This effectively ended “the 28-year reign of ordinary personal computers finding these huge prime numbers,” per the statement. GPUs can process large amounts of information simultaneously, so they are also used in artificial intelligence computing.

“It was a pretty big surprise, but I had been working hard to grow the system, so stayed aware of a relatively decent chance,” Durant tells New Scientist’s Matthew Sparkes. “I joined for a lot of reasons, in part to learn more about big math and information, show GPU capabilities at traditional computing and support some tremendous software and technology developed by the GIMPS community.”

In part, Durant wanted to show that GPUs—which he worked on developing as an engineer at NVIDIA—can be used for more than just A.I.

On October 11, an NVIDIA A100 GPU in Dublin, Ireland, flagged M136279841 as a potential prime number using the Fermat probable prime test. The next day, an NVIDIA H100 in San Antonio confirmed the finding with a primality test called the Lucas-Lehmer test, per the statement. After some debate, GIMPS opted to use October 12 as the official date of Durant’s discovery.

The largest prime number: 2¹³⁶²⁷⁹⁸⁴¹-1 https://t.co/Bo6ThyWjSx pic.twitter.com/yNILZ6KYKz

— Prof B Buchanan OBE FRSE (@billatnapier) October 21, 2024

Large prime numbers can play a role in cryptography algorithms used to protect data in applications such as online banking and private messaging services, Vishwam Sankaran reports for the Independent.

Beyond the thrill of the discovery, however, the practical use for M136279841 is almost nonexistent. Put simply, “it’s entertainment for math nerds,” George Woltman, co-founder of GIMPS, tells the Washington Post’s Ben Brasch.

In the future, though, that could change. “There’s no use for extremely large prime numbers now, but it’s not at all inconceivable that one day somebody will find something,” Kevin Buzzard, a mathematician at Imperial College London, tells New Scientist. “And then they’ll look at the maths research community and say, ‘So, where are your very large prime numbers?’ and they’ll say, ‘Well, actually, we’ve been thinking about that for decades.’”

For now, GIMPS volunteers are already working to beat this fresh record, and the stakes are higher for future finds. The discoveries of the first hundred-million-digit prime and billion-digit prime will be awarded $150,000 and $250,000, respectively.

Durant plans to donate his $3,000 winnings to the math department at the Alabama School of Math and Science, the public boarding school that he went to before Caltech.

Margherita Bassi | READ MORE

Margherita Bassi is a freelance journalist and trilingual storyteller. Her work has appeared in publications including BBC Travel, Discover magazine, Live Science, Atlas Obscura and Hidden Compass.