Move aside \(2^{82,589,933}-1\); there’s a new prime juggernaut in town. Researchers have identified \(2^{136,279,841}-1\) as the largest known prime number, surpassing the former record-holder by over 16 million digits. This monumental discovery was made possible through the advanced computing technology of Nvidia.
The newly discovered number is abbreviated as M136279841, simplifying discussions around it. It’s calculated by multiplying two together 136,279,841 times and then subtracting one. This number marks only the 52nd known Mersenne prime, a special class of primes studied by the monk Marin Mersenne in the early 1600s.
Luke Durant, a researcher and former Nvidia employee, played a key role in this discovery as he is the most prolific contributor to the Great Internet Mersenne Prime Search (GIMPS). GIMPS, which first discovered its initial Mersenne prime in 1996, has found the last 18 Mersenne primes. This is thanks to volunteers utilizing a free program to search for them.
Durant utilized a supercomputer composed of thousands of GPUs across 17 different countries, starting with an Nvidia A100 in Ireland and later confirming the discovery with an Nvidia H100 in Texas. For his efforts, Durant will receive a $3,000 reward from GIMPS.
Why are prime numbers relevant
Prime numbers are numbers which have no positive integer divisors other than 1 and themselves, according to Wolfram Math World. They are essential in number theory. The latest find underscores the capabilities of modern computing in mathematics. While current practical uses for such large Mersenne primes remain limited, the landscape may shift. Similar doubts existed decades ago until significant cryptographic algorithms were developed based on prime numbers.
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The identification of primes involves the Fermat probable prime test, followed by the rigorous Lucas-Lehmer primality test. The GIMPS team decided to officially recognize the discovery date based on the Lucas-Lehmer test.
As an incentive for future discoveries, GIMPS offers a $150,000 prize for the first hundred-million digit prime and $250,000 for the first billion-digit prime. This recent find exemplifies not just a thrilling mathematical achievement but also showcases the robust capabilities of cloud supercomputers and networks of GPUs like those that led to M136279841’s discovery.
