On January 7, a network of volunteers rang in the new year by discovering the largest known prime number in history, now known as M74207281. Although a mouthful in its own right, M74207281 is short for 274,207,281-1, a number with 22.3 million digits. The new number was found by members of the Great Internet Mersenne Prime Search (GIMPS) and is over 5 million digits larger than the last prime, which was discovered by GIMPS in 2013. Among these members was Aerospace Engineering alumnus Ernst Mayer (Ph.D. ’93), whose MLucas software was used to verify the primality of the new Mersenne prime.
Founded in 1996 by George Woltman, GIMPS is a group of mathematics and computer science enthusiasts who use freely available software to try and calculate the largest known primes. Specifically, the group is after a special class of numbers, Mersenne primes, and generates over 450 trillion calculations per second on their quest.
Mersenne primes, named after the French monk who studied them in the 17th century, take the form 2n-1. Though they have been discussed since 300BC, only 49 primes have been discovered, and GIMPS members have found the most recent 15.
When Mayer stumbled upon GIMPS in the late 1990s, he was an assistant engineering professor at Case Western Reserve University. He found the group while looking for novel ways to teach his students the Fast Fourier Transform algorithm, which the GIMPS software utilizes to multiply together massive integers (more on FFT algorithms). Fascinated, he began working on his own code for testing Mersenne primality. Many years, lessons in C/C++ and assembly programing, and lines of code later, Mayer had developed MLucas, the world’s second fastest Mersenne prime code for Intel x86 computer architecture.
"Getting here has been a fascinating and dare I say unique learning experience"Ernst Mayer
“Being where I am code-wise permits the privilege of being party to the independent verification of any new prime,” Mayer reflected, “and getting here has been a fascinating and dare I say unique learning experience.”
In addition to his work with GIMPS, Mayer researches another class of numbers, Fermat numbers, that take the form 2^(2n) +1. In the late 1990s, he collaborated with Richard Crandall, who developed an algorithm on which the GIMPS software is based, and together they tested the primality of the 24thFermat number. At the time, this 5 million digit figure was the largest ever subjected to such an extensive test. Mayer is currently trying to improve his code’s basic algorithm so that it may one day test the now-smallest such number of unknown character, the 33rd Fermat number, which has over 2.5 billion digits – over 100 times as many as the new Mersenne prime.
“Given that folks like me… who are not doing nuclear-weapons design, climate modeling, or high-frequency stock trading do not get dedicated access to true ‘big iron’ supercomputers, this is of course a major challenge,” Mayer admitted. “Nonetheless, I optimistically estimate that the needed compute power will become available around roughly 2025. In the meantime, there is still lots of coding and number-crunching work to do!”
That there is. Though the new prime was just discovered, the hunt is already underway for the next number. Congratulations to Dr. Ernst Mayer and GIMPS for their incredible accomplishment! To learn more about the discovery and the organization, read more in Scientific Computing.