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 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.
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.”
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.
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.
Interview Between Time.news Editor and Dr. Kevin Buzzard on Luke Durant’s Discovery of the Largest Known Prime Number
Editor: Good morning, Dr. Buzzard! Thank you for joining us today to discuss the recent breakthrough by Luke Durant in the world of prime numbers. To begin, can you tell our readers why prime numbers are considered significant in mathematics?
Dr. Buzzard: Good morning, and thank you for having me! Prime numbers are fundamental building blocks in mathematics. A prime number is a whole number greater than 1 that has no positive divisors other than 1 and itself. They play a vital role in number theory and have implications in fields like cryptography, computer science, and even quantum physics. Each discovery helps us understand the nature of numbers better.
Editor: Luke Durant’s recent discovery is especially fascinating because it is the first major finding in almost six years. Can you elaborate on what makes his discovery, M136279841, so exceptional?
Dr. Buzzard: Certainly! M136279841 is notable not just for being the largest known prime, with over 41 million digits, but also because it is classified as a Mersenne prime. These primes are denoted in the form of 2^p – 1, where p itself is a prime number. They are rarer than other types of primes, and Luke’s discovery marks the 52nd known Mersenne prime. This illustrates a significant leap in our understanding of large primes, especially in the context of computational capabilities.
Editor: Speaking of computation, Luke utilized the Great Internet Mersenne Prime Search (GIMPS) to make his discovery. How has GIMPS changed the landscape of discovering prime numbers?
Dr. Buzzard: GIMPS represents a remarkable evolution in the way we explore primes. By leveraging distributed computing, it allows volunteers worldwide to contribute to the search for large primes using their personal computers. This democratization of mathematical discovery helps propel the field forward, enabling discoveries that might otherwise be unachievable with limited resources. It’s a great example of citizen science in action.
Editor: Luke mentioned wanting to “push the boundaries of the known universe” through his work. What does that mean for the future of computing and mathematics?
Dr. Buzzard: It speaks to the human drive to explore and innovate. The relationship between computing power and mathematical discovery is profound; every time we push the limits of what computers can do, we gain new insights into both technology and mathematics. Each large prime found serves as a milestone in documenting our progress in these areas.
Editor: George Woltman from GIMPS called Durant’s find a “rare and beautiful gem.” Do you believe there is intrinsic value in these discoveries, even if they have no immediate practical applications?
Dr. Buzzard: Absolutely! In mathematics, the joy of discovery is often as valuable as the application. Large primes, like beautiful art, inspire curiosity and provoke thought about the nature of numbers and the universe. They can stimulate interest in mathematics and inspire future generations of mathematicians, engineers, and scientists.
Editor: Lastly, can you explain the technical aspect of how GIMPS verifies the primality of such large numbers?
Dr. Buzzard: GIMPS uses advanced algorithms for primality testing, such as the Lucas-Lehmer test specific to Mersenne primes. When a probable prime is found, the GIMPS server is notified, and multiple tests are conducted on different hardware to confirm its primality. This rigorous verification process is essential for ensuring that the discovery is legitimate.
Editor: Thank you so much for sharing your insights today, Dr. Buzzard. It’s been a pleasure discussing this incredible achievement in the field of mathematics!
Dr. Buzzard: Thank you for having me! It’s always exciting to talk about the wonders of prime numbers and the intriguing journeys of discovery.