Record-breaking prime number containing more than 41 million digits found by former Nvidia programmer

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For many people, prime numbers have faded into the background since distant grade school days. However, for Luke Durant, a 36-year-old former Nvidia programmer, prime numbers became an all-consuming passion. He devoted nearly one year and invested a considerable sum of his own money to uncover the world’s largest known prime number.

If you need a refresher, a prime number is a whole number that can only be divided by 1 and itself, such as 2, 3, 5 and 7. Durant’s remarkable discovery, officially called M136279841, consists of an astounding 41,024,320 digits and marks the first prime breakthrough in almost six years.

The historic finding is classified as a Mersenne prime, which is named after the French monk Marin Mersenne, who studied these numbers more than 350 years ago. Mersenne primes are a rare kind of number, making Durant’s finding of the 52nd known Mersenne prime even more impressive. A number is only considered a Mersenne prime if it can be written in the form 2ᵖ-1.

Unlike other large prime numbers used in some applications to protect internet security, Mersenne primes are important for other reasons. “The historical record of the world’s largest prime tells us something about the historical capability of computers, and in particular it tells us something about the progress of humanity in this area,” said Dr. Kevin Buzzard, professor of pure mathematics at Imperial College London who was not involved in Durant’s efforts.

The Great Internet Mersenne Prime Search, or GIMPS, a community-based project, announced Durant’s breakthrough on October 21. GIMPS is an example of citizen science, which according to Buzzard allows nonspecialists to make some of the discoveries of the largest known primes.

“I recognized that the GIMPS community has put together an incredible system with amazing technology for searching for huge prime numbers,” said Durant, who is based in San Jose, California. After familiarizing himself with the project’s software and learning how to use cloud computers, he skillfully combined these elements, enabling him to run enough worldwide systems to create an incredibly speedy supercomputer.

The GIMPS community includes volunteers from around the world who run the project’s software on their personal computers in search of new primes and mathematicians who analyze Mersenne results to expand future exploration.

What inspires thousands of volunteers to hunt for the world’s largest primes? For Durant, it’s a combination of his interests in developing large computing systems and exploring the limitations of the laws of physics, specifically the restrictions on the content and speed of computing. “I wanted to push the boundaries of the known universe in whatever small way I was able,” he said. “These enormous prime numbers are, in some senses, the largest ‘unique pieces of information’ in the known universe.”

The hunt for ever-larger prime numbers

While there are no practical applications for such astonishingly large prime numbers today, that does not diminish the significance to those involved in the project. “This find is more of a novelty item to math folks a rare and beautiful gem,” said George Woltman, the founder of GIMPS, who has been running the collaborative project as a hobby for 28 years, in an email. “Maybe (the program’s) best use will be inspiring the next generation of young mathematicians.”

Durant received a preliminary alert of his prime advancement on the evening of October 12 while finalizing packing for a trip. “I took a moment to decide if I felt up to work on it immediately to confirm the new number to be prime,” he said, “before deciding it was too important to let linger and sat down to get back to work.”

To test the primality of a number, the GIMPS programs run a probable prime test, and, if the test produces a successful result, the number is almost conclusively a new prime number. From there, the GIMPS server is notified, and several definitive primality tests are run on different hardware and programs to verify the new Mersenne prime.

Even for an experienced programmer such as Durant, the finding was exhilarating. “I’m extremely fortunate to be the discoverer for the most recent Mersenne prime number,” he said. “These numbers are so exceptionally large and rare now that I was fully prepared to fail after maybe still another year or two of effort.”

What’s more, Durant’s feat is notable as the first of its kind uncovered through graphics processing units, or GPUs, according to GIMPS. GPUs are known for performing mathematical equations at high speeds and processing many pieces of data simultaneously; they are in everyday devices such as smartphones or laptops, rendering high-quality graphics or training artificial intelligence networks to process extensive amounts of information efficiently.

Unlike previous successful Mersenne prime searches that used central processing units, or CPUs, the primary component of a computer that serves as its control center to run the machine’s operating system and apps, Durant’s use of graphics processing units transformed his experience. Programmer Mihai Preda helped paved the way for Durant’s discovery after he wrote the GpuOwl software, which has been available for all GIMPS users to test for Mersenne primality since 2017.

The professional-grade GPUs that Durant employed are known for their efficiency in handling repetitive math calculations in seconds. Durant’s supercomputer also included thousands of server GPUs, crossing 24 data center regions over 17 countries, according to a statement GIMPS released.

Woltman predicts that more primes will be discovered using GPUs in the future.

“GPUs are so good at tackling difficult number crunching compared to CPUs which are suited to a wide variety of problems,” he said. “That said, don’t count CPUs out, they will still be an important part of GIMPS and may well find the next prime number.”

Durant credits much of his success to the education he received at the Alabama School of Mathematics and Science in Mobile and its supportive environment. “My interests and technical abilities are in no small part due to my fellow students and faculty at ASMS,” he said.

Based on his new Mersenne prime advancement, Durant is eligible for the $3,000 GIMPS research discovery award. He said he plans to donate his prize money to the public high school. “I’m glad to have a result that can help show a little bit about a special place in the South,” he said.

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