A massive discovery has sparked calculated excitement in the maths world: the record for the highest prime number ever has been broken.
A prime number can only be divided by 1 and itself. For example, the number 23 is prime because if you divide by 1 you get 23, and if you divide by 23 you get 1 – but dividing by anything else doesn’t give you a whole number.
So what is the new prime number? It’s not one for your pocket calculator: 2136,279,841-1 (known to its friends as M136279841). At 41,024,320 digits long, the new prime number is 16 million digits larger than the previous record holder. Presuming you can read two digits a second, it would take 237 days in total just to read M136279841 in full.
What’s more, it’s a special kind of prime: a Mersenne prime. These are prime numbers in the form 2P-1. Essentially, you take a number (represented here as P) and multiply the number 2 by that many times – and then minus 1.
For example, the number 31 is the Mersenne prime 25-1, because if you multiply 2 five times (2 x 2 x 2 x 2 x 2) you get 32, and when you minus 1, you get 31.
Easy, right? But the new prime number, M136279841, is a little bigger. For this one, you multiply together 136,279,841 twos, and then subtract 1. The discovery makes this the 52nd Mersenne prime ever discovered.
“We know that there are an infinite number of prime numbers… though interestingly we are currently unable to prove that there are an infinite number of Mersenne primes, which I think it rather exciting,” said Sophie Maclean, PhD student in analytic number theory at King’s College London.
M136279841 was the hardest-to-find Mersenne prime yet. Detected by the 36-year-old prime seeking volunteer Luke Durant, 2136,279,841-1 was found using free software available from the Great Internet Mersenne Prime Search (otherwise known as, ahem, GIMPS).
So how did he do it? For the first time in 28 years, this prime was not discovered using a personal computer, but rather a graphics processing unit (GPU). Yep, that’s right – the powerful processors widely used for artificial intelligence (AI) are also used in maths and science research.
Durant essentially created a cloud-based supercomputer to run the GIMPs software across thousands of server GPUs (spanning 24 data centres in 17 countries).
For this incredible feat, Durant won a $3,000 reward, which he plans to donate to the Alabama School of Math and Science.
New prime numbers themselves aren’t that significant to maths, Maclean explains: “I kind of view it like collecting rare Pokémon. It's super fun to do, and if they are very rare then you want to be one of the few people to find them, but outside of the game, it isn't a huge feat of intellect.”
But Mersenne primes are different. “What I would be most interested in would be for there to be more discovered about Mersenne primes,” said Maclean.
“Finding prime numbers is very fun and exciting, but for me, the real cool things lie in why: Why are Mersenne primes so rare? Can we narrow down further which Mersenne numbers are likely to be prime? There is still a lot to explore and I can't wait!”
About our expert
Sophie Maclean is a PhD student in analytic number theory and additive combinatorics at King’s College London. She has spoken at the Royal Institution and Cheltenham Science Festival, and has presented videos on the Numberphile YouTube channel.
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