Amateur sleuth finds largest known prime number with 41 million digits

After a six-year drought, we now have a new largest known prime number, thanks to an amateur mathematics sleuth who deployed an army of graphics processing units (GPUs) to crunch through the possibilities.

Prime numbers are those divisible only by 1 and themselves, such as 2, 3 and 5.  There are an infinite number of primes, but proving which numbers are actually prime becomes harder the larger they get. We can now add 2^136,279,841-1 to the list, which at 41,024,320 decimal digits long is the biggest prime number currently known.

It was discovered by a relatively new member of a group called the Great Internet Mersenne Prime Search (GIMPS), where thousands of people have downloaded software to hunt for prime numbers. Those lucky enough to discover one earn a place in prime number history, but also a $3000 prize. This is the first prize to be awarded since 2018.

The new prime number, labelled by the GIMPS group as M136279841, was found by Luke Durant, who formerly worked for Nvidia as an engineer developing GPUs, and has been searching for big primes for just under a year.

All previous GIMPS discoveries were made by computer CPUs in relatively humble personal computers, but Durant’s past at Nvidia exposed him to GPUs – the chips originally designed for powering computer games but also key to the recent rise in AI computing. He believed they would be ideal for hunting prime numbers and took advantage of a GPU system for its number-crunching abilities. He networked thousands of GPUs housed in 24 data centres across 17 countries, and has been described by the GIMPS project as a “prolific contributor”.

“It was a pretty big surprise, but I had been working hard to grow the system, so stayed aware of a relatively decent chance,” says Durant. “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.”

The new prime is the 52nd of a specific type called Mersenne primes to ever be discovered. Named for the French monk and mathematician Marin Mersenne, these primes are exactly one less than a power of two – which makes them slightly easier to find, and therefore the focus of GIMPS.

Kevin Buzzard at Imperial College London says there is absolutely no practical application for the finding, but that the same can initially be said for lots of mathematical research. “There’s no use for extremely large prime numbers now, but it’s not at all inconceivable that one day somebody will find something,” says Buzzard. “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…’.”