This latest record-breaking prime number takes 237 days to read

A huge discovery has caused computational excitement in the mathematics world: the record for the highest prime number of all time has been broken.

A prime number can only be divided by one and itself. For example, the number 23 is a prime number because when you divide by 1 you get 23, and when you divide by 23 you get 1 – but dividing by anything else doesn’t make a whole number.

So what is the new prime number? It’s not for your calculator: 2^136,279,841-1 (known to his friends as M136279841). With a length of 41,024,320 digits, the new prime number is 16 million digits larger than the previous record holder. Assuming you can read two digits per second, it would take a total of 237 days to completely read M136279841.

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Furthermore, it is a special type of prime: a Mersenne prime. These are prime numbers in the form 2^P-1. Essentially, you take a number (represented here as P) and multiply the number 2 that many times – and then minus 1.

For example, the number 31 is the Mersenne prime number 2⁵-1, because if you multiply 2 five times (2 x 2 x 2 x 2 x 2) you get 32, and if you minus 1 you get 31.

Easy, right? But the new prime number M136279841 is slightly larger. To do this, multiply 136,279,841 twos and then subtract 1. The discovery results in 52^nd Mersenne prime ever discovered.

“We know that there are infinitely many prime numbers… although interestingly, we are currently unable to prove that there are infinitely many Mersenne prime numbers, which I find quite exciting,” said Sophie Maclean, a doctoral candidate in analytic number theory at the King’s College London University.

M136279841 was the hardest Mersenne prime number to date. Discovered by 36-year-old volunteer Luke Durant, 2nd^136,279,841-1 was found using free software available from Great Internet Mersenne Prime Search (aka, er, GIMPS).

So how did he do it? For the first time in 28 years, this Prime was discovered not with a personal computer, but with a graphics processing unit (GPU). Yes, that’s right – the powerful processors commonly used for artificial intelligence (AI) are also used in math and science research.

Durant essentially built a cloud-based supercomputer to run the GIMPs software on thousands of server GPUs (in 24 data centers in 17 countries).

For this incredible achievement, Durant won a $3,000 reward, which he plans to donate to the Alabama School of Math and Science.

New prime numbers in themselves are not that important for mathematics, explains Maclean: “For me, it’s like collecting rare Pokémon. They’re super fun to make, and when they’re super rare you want to be one of the few to find them, but outside of the game it’s not much of an intellectual achievement.”

But Mersenne primes are different. “What I would be most interested in is learning more about Mersenne primes,” Maclean said.

“Finding prime numbers is a lot of fun and exciting, but for me the really cool thing is why: Why are Mersenne primes so rare?” Can we further narrow down which Mersenne numbers are likely primes? There’s still a lot to discover and I can’t wait!”

About our expert

Sophie Maclean is a PhD candidate in analytic number theory and additive combinatorics at King’s College London. She has given talks at the Royal Institution and the Cheltenham Science Festival and presented videos on the Numberphile YouTube channel.

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