New Largest Prime Discovered!
A new world record breaking Prime Number has been discovered by American Prime Hunter Luke Durant in October 2024 after he invested around 2 million dollars of his own money in the quest to find a new Largest Prime.
It has been six years since the record was last broken and the newly discovered gigantic Prime is a whopping 41 million digits long. The new number is a special type of Prime called a Mersenne Prime and Luke Durant has now gone down in history as the discover of the 52nd Mersenne Prime.
Image by Gerd Altmann from Pixabay
Mersenne Primes
Mersenne Primes are of the form 2n - 1 and even though Luke’s Prime has 41 million digits, it is easy to write down:
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New Largest Prime discovered October 2024 by Luke Durant
2136279841 - 1
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(This Mersenne Prime also has the label M136279841)
It is important to note that most numbers of the form 2n - 1 are not Mersenne Primes, for example 24 - 1 = 15 which is not prime. Prime Hunters are looking for values of n which make 2n - 1 prime, and only 52 Mersenne Primes have been found so far. They are super rare!
Great Internet Mersenne Prime Search
Up until 1951, new Mersenne Primes were calculated by hand. When famous mathematician Leonhard Euler discovered the 8th Mersenne Prime in 1776, he did simply not have the luxury of using a computer. After 1951 discoveries of new Mersenne Primes began to be made using newly emerging computer technology. In 1996 there was a radical shake up of the world of Prime hunting, as this was the year that saw the launch of the Great Internet Mersenne Prime Search (GIMPS).
The idea was simple – anyone with an ordinary home computer could start hunting for primes by using the freely available GIMPS software. The Great Internet Mersenne Prime Search led to the formation of a huge community of people around the world who were looking for Mersenne Primes. Amazingly, you can still join the search today by visiting the GIMPS website and using your home computer to hunt for Primes.
Luke’s Mersenne Prime Discovery
Luke Durant decided to take the Great Internet Mersenne Prime Search to the next level. Luke formed a cloud-based supercomputer using GPUs which could do a large number of calculations simultaneously, using 24 different data centres scattered across the world. The remarkable thing is that Luke was doing this as a hobby, and that he invested around $2 million of his own money to keep the supercomputer running. Luke Durant had previously spent 10 years working for tech giant Nvidia and was able to use these skills to power his quest for the next biggest Prime. Despite Luke’s gargantuan computing power, it is important to emphasise that ordinary people can still use their own computers as part of the Great Internet Mersenne Prime Search. Everyone is wondering – how long will it take to beat Luke’s record? Will it be another six years, or could it be a lot sooner?
Photo by Elham Abdi on Unsplash
Mersenne Primes and Perfect Numbers
Once you have found a new Mersenne Prime, you get a new Perfect number for free. Perfect numbers are really special as they are equal to the sum of their proper divisors. The smallest perfect Number is 6: this is because 6 = 1 + 2 + 3, the sum of its proper divisors. There is a very important connection between Mersenne Primes and Perfect Numbers (see the Euler-Euclid Theorem for more details). If you have a Mersenne Prime of the form 2n - 1 then there will be a related Perfect Number 2(n-1)(2n - 1). The discovery of the new 52nd Mersenne Prime means that a new Perfect number has also been found, with over 82 million digits. If you want to write down this new perfect number, then the start and the end of it looks like this: 388692...008576.
Photo by Maximalfocus on Unsplash
Do we need a new Largest Prime?
In general, Prime Numbers are very useful and play an important role in encrypting our messages and securing our online transactions. Despite this, finding a new Largest Prime currently does not have any particular known use, so why bother? If you are interested in what motivated Luke to get involved in finding Prime numbers then you can watch an interview with him on the Numberphile YouTube channel. He certainly doesn’t seem motivated by money as he kindly donated his $3,000 prize money to the Alabama School of Math and Science. (Yes, that’s right - if you discover a new Mersenne Prime you are also awarded Prize Money of at least $3,000!)
The truth is that people throughout history have always loved the thrill of discovery. Being the first to climb a mountain, trek to the South Pole or step on the Moon is too hard to resist and finding a new undiscovered Prime is no different! Over the years many discoveries have also been thought useless or frivolous, but there have been unintended benefits or advances. The moon landings alone spawned lots of unintended inventions such as vacuum-packed food. It may be ‘watch this space’ in terms of how the 52nd Mersenne Prime might be used in the future.
Photo by Ethan Sees
Further Watching and Reading
The Man Who Found the World's Biggest Prime – Numberphile
An interview with Luke Durant who made the discovery.
Matt Parker Video on New Largest Prime Number
As well as giving lots of interesting background on the discovery, this video scrolls through all 41,024,320 digits of the new prime, allowing you to see it with your own eyes.
Article in BBC Science Focus Magazine
Find out more about the new Mersenne Prime M136279841, including the fact that it would take 237 days to read it in full.
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