Recently, both the largest Mersenne prime and the largest prime in general was found; this is a very important discovery in the mathematical area of number theory. This was the 52nd Mersenne prime ever found, and between the 51st and 52nd, it took mathematicians using specialist software 7 years.
A Mersenne prime is a prime number of the form 2p – 1, where p is a pre-existing prime number. To start with, these numbers are small, the first three being 3, 7, and 31 but very quickly ramp up, with the 10th Mersenne prime already reaching 27 digits. In 1995, in an effort to find these huge numbers, the Great Internet Mersenne Prime Search (GIMPS) was set up to corroborate efforts by several mathematicians as well as releasing free software for the sole purpose of finding Mersennes. Unexpectedly, the mathematician who found its latest discovery only joined the search in October 2023.
Luke Durant, an ex-NVIDIA employee turned researcher, was the person responsible for the discovery; he did this by creating a “cloud supercomputer” of GPUs globally, all simultaneously using the GIMPS software. This resulted in the discovery of a prime number 16 million digits larger than the 51st Mersenne prime, resulting in a 41 million-digit number I can’t even begin to imagine. But in the form mentioned earlier, this is represented as 2136,279,841 – 1.
New prime numbers are a very relevant concept with applications within mathematics and computer science. After the searching process, these numbers need to be checked since the Fermat probable prime test used in the preliminary test is relatively simple and these calculations have many stages where it can go wrong. For example, the 49th Mersenne prime, 274,207,281 – 1, took roughly 34 quadrillion steps. Checking these primes helps consolidate otherwise hard-to-verify algorithms as well as being a great test for hardware.
In mathematics, and specifically number theory, prime numbers have always been an area of great interest. Mersenne primes have a particular link to perfect numbers; these are numbers where the number itself is equal to the sum of all its divisors. This tells us that if 2p – 1 is a prime, then 2p – 1(2p – 1) is a perfect number. There aren’t many real-life applications of this but it’s important to understand how these groups of numbers interact.
Durant received $3000 for this discovery but is choosing to donate his prize towards the Alabama School of Math and Science, giving funds back to the institution originally behind the search.
