M136279841: New largest known Mersenne prime number confirmed with GPU

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The news that a new largest prime number has probably been discovered has been making the rounds in mathematician circles for a few days now; the result has now been confirmed. The "Great Internet Mersenne Prime Search" (GIMPS) project has found the 52nd Mersenne prime number M136279841, six years after the discovery of the 51st: 2^136,279,841-1 with an impressive 41,024,320 digits is the new largest known prime number. Luke Durant, a 36-year-old researcher and former Nvidia employee from San José, found the number on October 12, 2024 using GPUs. The prime number was first identified as probably prime by an Nvidia A100 GPU in Dublin and then definitively confirmed by another Nvidia H100 in San Antonio, Texas, using a Lucas-Lehmer test. Subsequently, the 52nd Mersenne prime was verified using various other methods on different independent systems. This process lasted until October 19. The newly discovered number is the 18th Mersenne prime that GIMPS has found since its launch in 1996. If you would like, you can download a ZIP archive containing the 41,024,320 digits.

End of an era: GPUs replace CPUs

This discovery marks the end of a 28-year era in which conventional PCs found these huge prime numbers. In 2017, Mihai Preda developed the GpuOwl program to use the computing power of GPUs to test Mersenne numbers for their prime properties (primality) and made it available to GIMPS users.

Durant recognized the potential of GPUs and developed an infrastructure to run GIMPS software on many GPU servers. In October 2023, he began contributing to the GIMPS initiative, taking advantage of the increasing availability of GPUs in the cloud, from which he built a "cloud supercomputer" infrastructure with thousands of server GPUs in 24 data centers in 17 countries, according to the GIMPS project press release.

What are Mersenne primes?

Mersenne primes, named after the 17th century French monk Marin Mersenne, have the form 2^p-1, where p itself is a prime number. Euclid already proved that every Mersenne prime generates a perfect number. A perfect number is a number whose real divisors add up to the number itself. The new largest perfect number is 2^136,279,840 × (2^136,279,841-1) and has over 82 million digits.

Mersenne primes play a central role in number theory and have practical applications in cryptography. Each Mersenne prime generates a perfect number, which makes it particularly interesting for mathematicians. The newly discovered prime number generates a perfect number with more than 82 million digits.

Crowdsourcing success GIMPS

Founded in 1996 by George Woltman, GIMPS uses the collective computing power of thousands of ordinary computers worldwide. Volunteers can download the software for free to participate in the research and have the chance to win a research grant of 3,000 US dollars. The project is continuing its search for more Mersenne primes and invites anyone interested to join in the hunt for these mathematical rarities.

Durant emphasized that the discovery shows the versatility of graphics processors, which make a decisive contribution not only to artificial intelligence, but also to mathematical and scientific research.

(vza)