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The Discovery of the Largest Known Prime Number

Prime numbers, which can only be divided by one and themselves, have intrigued mathematicians for centuries. In the 17th century, the French monk and mathematician Marin Mersenne formulated a method to identify these numbers, identified by values such as two, three, five, and seven. Although there are infinitely many prime numbers, locating larger ones can become significantly more complex.

Mersenne established a simple yet effective technique known as Mersenne primes, which involves subtracting one from powers of two. For instance, three is derived from two squared minus one, and seven from two cubed minus one. However, not all prime numbers can be expressed in this form.

Recently, a major advancement in this realm was achieved by Luke Durant, a researcher and former employee of NVIDIA, who discovered the 52nd Mersenne prime, the largest known prime number to date: 2^136,279,841 minus one. This immense number, designated M136279841, boasts an astonishing 41,024,320 decimal digits, surpassing the previous record by 16 million digits. This significant achievement was made public through a statement from the Great Internet Mersenne Prime Search (GIMPS) on Monday.

GIMPS is a collaborative project composed of volunteers who utilize free software to seek out Mersenne primes. Since its inception in 1996, the organization has discovered the last 18 Mersenne primes, rewarding each contributor with a $3,000 prize. Since joining GIMPS in October 2023, Durant has emerged as its “most prolific contributor,” according to their announcement.

To uncover M136279841, Durant employed GIMPS software along with a supercomputer architecture consisting of thousands of graphics processing units (GPUs) distributed across 24 data centers globally. This endeavor marked the end of what had been a 28-year period where traditional personal computers facilitated the discovery of significant prime numbers, as stated by GIMPS. Given their ability to process vast amounts of data concurrently, GPUs are also instrumental in artificial intelligence applications.

“It was quite unexpected, though I was fully aware of a decent probability,” Durant mentioned in an interview with New Scientist‘s Matthew Sparkes. He expressed his intention to contribute to the mathematical community, showcase the capabilities of GPUs beyond their traditional roles, and support the influential software developed by the GIMPS team.

On October 11, a GPU in Dublin raised the suspicion that M136279841 might be a prime number using the Fermat probable prime test. The subsequent day, a GPU in San Antonio confirmed its primality with the Lucas-Lehmer test. GIMPS ultimately set October 12 as the official date of Durant’s discovery.

The newly identified M136279841 holds interest not just as a mathematical curiosity; large prime numbers like it have applications in cryptography, playing a vital role in securing data for online banking and private messaging services, as noted by Vishwam Sankaran in the Independent.

Despite its record-setting nature, experts emphasize that the practical application of M136279841 is minimal. According to George Woltman, co-founder of GIMPS, it serves primarily as “entertainment for math enthusiasts.” However, there is speculation that such large primes could eventually find utility in unforeseen ways. Mathematician Kevin Buzzard articulated that while currently there may be no practical use, the future may reveal needs for these numbers in mathematical research.

Future discoveries promise even more substantial rewards, as GIMPS has announced a $150,000 prize for the first hundred-million-digit prime and a $250,000 prize for a billion-digit prime.

In a display of generosity, Durant has indicated that he intends to donate his $3,000 prize to the mathematics department at the Alabama School of Math and Science, the public boarding school he attended prior to his studies at Caltech.

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