A relative newcomer to the Great Internet Mersenne Prime Search (GIMPS) has broken a six-year drought in the search for the next prime oasis in a desert of boring ol’ composite numbers.
At an insane 41,024,320 decimal digits in length, writing the entire number would take months to write in full. To keep things brief – if a little harder to appreciate – it is 1 fewer than the result of the number 2 raised to the power of 136,279,841. Or, to use its official title, it’s called M136279841.
Former NVIDIA employee, Luke Durant, only began contributing to the search in October last year, though had a little more going for him than beginner’s luck. Durant made use of thousands of graphics processing unit servers spanning 24 datacenter regions in 17 different countries to run the software on his behalf.
On October 11 this year, a server in Dublin landed on M136279841 as a contender. A day later, another server in Texas gave the digital thumbs-up, confirming its legendary status as the new mathematical Optimus Prime.
Primes are counting numbers greater than 1 that aren’t products of two smaller numbers. At first glance, they seem rather unassuming, with 2, 3, and 5 sharing space on the number line with integers like 4 and 6, which can be constructed through simple multiplication.
Yet as we count ever higher, numbers that can’t be divided so cleanly get harder to find, leading to the question of whether it’s possible they eventually run out.
To spare you the indignity of taking off your socks and starting the count yourself, the answer is no. Primes are an infinite resource. Not that it makes them any easier to locate.
Strip away the legion of fancy hardware employed by Durant and his peers, monster-prime hunting hasn’t changed a great deal since the 17th-century French friar Marin Mersenne turned his attention to these notable numbers and left his name imprinted on a method for finding primes of a particular flavor.
‘Mersenne primes‘ are those that take the form 2n – 1. Not all numbers in this format are primes, of course. For example, 2 x 2 x 2 x 2 = 16, with 1 fewer equalling 15 (a composite of 3 and 5). And not all primes are of the Mersenne variety.
But given this approach is efficient at finding numbers that are prime, and the fact it can be tested with relative ease, it’s become the method of choice by collaborations like the GIMPS, which since it was founded in 1996 has sifted 18 of the numerical gems from the vast sand dune of composites, bringing the total known to 52.
The previous record holder – discovered in 2018 by Patrick Laroche from Ocala, Florida, who removed 1 from 2 to the power of 82,589,933 to calculate it – is just shy of 25 million digits in length. Laroche ran the free prime-searching program on his own hardware, meaning Durant’s success using a network of GPUs represents a new era in the search for Mersenne primes.
So why go to the trouble of spotting such massive numbers in the first place? Fame, bragging rights, and a chance to win cash awards aside, not a great deal.
As co-founder of the GIMPS, George Woltman, told Ben Brasch at The Washington Post, “It’s entertainment for math nerds.”
Big primes are handy for a type of encryption, admittedly, though with the digital safe-cracking power of quantum computing on the horizon, those days might be – shall we say – numbered.
Considered as the atoms of all positive integers, primes have a beauty all of their own. No doubt a brand new Mersenne prime will soon emerge on expanding banks of ever-smarter technology around the world.
It will be number 53 on the list. A prime number.