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Last October, an amateur mathematician named Luke Durant discovered the largest known prime number, M136279841, a number with more than 41 million digits. Luke used a global network of computers powered by Graphics Processing Units (GPUs), which are widely used in developing artificial intelligence algorithms. Luke’s breakthrough marked the first use of this technology to uncover a prime of this size.

Prime numbers are special because they can only be divided by 1 and themselves. While smaller primes like 3, 11, and 37 are easy to conceptualize, larger primes have to be discovered through a complex and challenging process. “A billion is already an unfathomable number with just ten digits,” remarks Luke. To put the new prime’s size into perspective, he added, “It could be read aloud, but that would take several years. In a book, it would fill 15,000 to 20,000 A4 pages.”

What makes M136279841 even more special is that it’s a Mersenne prime, a rare type of prime named after a 17^th-century French monk named Marin Mersenne. Mersenne discovered a simple formula for finding primes: by raising the number 2 to the power of a prime number and subtracting 1 from the product. For instance, 2³ – 1 = 7. Luke’s discovery followed the same rule, only the prime number to which he raised 2 was mind-boggling: 2^136279841−1. The exponent is where the name M136279841 comes from.

Luke found this giant prime number as part of the Great Internet Mersenne Prime Search (GIMPS), a group of volunteers from around the world who use free software to hunt for huge primes. Since 1996, GIMPS has identified the last 18 Mersenne primes. In order to find this prime number, Luke used the GIMPS software and a supercomputer network with thousands of computer servers spanning 17 countries. Describing his year-long journey, Luke compared the process to “sifting grains of sand through a filter until you find the small pebble that doesn’t make it through.”

Finally, a breakthrough was achieved when a server in Dublin, Ireland flagged M136279841 as a potential prime. A server in San Antonio, Texas confirmed it the next day. After thorough verification, GIMPS officially recognized the discovery on October 12, 2024. This ended a six-year drought since the last Mersenne prime was found. Volunteers who find a new prime receive $3,000, which Luke plans to donate to his former school, the Alabama School of Math and Science.

But why do such massive prime numbers matter? Today, large prime numbers play a key role in modern cryptography and encryption. These services keep online information secure, like banking transactions and private messages. Although too large for current encryption systems, M136279841 showcases the power of GPUs and the potential for amateurs to achieve breakthroughs with advanced computational tools. Beyond practicality, the joy of uncovering something new continues to inspire and drive mathematical exploration. 

Anay Ashwin was an outstanding participant in Double Helix’s Young STEM Journalism Bootcamp. This year, Double Helix partnered with Letterly to launch the inaugural 4-week program, inviting students aged 8 to 18 to write science news articles on the topics that matter to them! This article went through multiple rounds of editing with 1-to-1 feedback from Letterly’s highly qualified and passionate writing coaches. Double Helix editors provided a final edit for accuracy and style.