Maths fans canāt get enough of numbers that are millions of digits long andĀ can only be divided by themselves and one. Now, through a collaborative effort, utilising computers distributed around the world, theyāve that the number 277,232,917 ā 1 is prime.
The discovery was initially made on 26th December by a computer volunteered by Jonathan Pace, as part of the Great Internet Mersenne Prime Search (GIMPS). Pace,Ā a 51-year old electrical engineer based in Germantown, Tennessee, has been hunting primes for over fourteen years and his belated Christmas present is eligible for a $3,000 reward from GIMPS.
The new prime number, known as M77232917, is one million digits larger than the previous record. It is also a particularly rare type of prime called a Mersenne prime, meaning that it is one less than a power of two.
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Three is a Mersenne prime because it is a prime and is equal to 22 ā 1. Other Mersenne primes include 7, 31, 127, and 8191. There are only fifty known in total, with the last sixteen discovered by GIMPS. Itās thought that there are an infinite number of Mersenne primes, but this has yet to be proven. This means the latest discovery could be the final Mersenne prime, although probably not.
Get hunting
Anyone can start searching for large Mersenne primes by . If you strike it lucky, not only is the discovery attributed to you, thereās also a cash prize. Proving that M77232917 is prime took Paceās computer six days of non-stop computation. Four other computers then verified the result.
Though prime numbers are used in many forms of cryptography ā the mathematics that keeps the internet secureĀ ā the latest discovery will be of no immediate practical use. āThere is not a particular concrete thing that you can do with massive primes. Instead itās about a quest to find something completely new,ā says Iain Bethune at , a website that crowdsources computing power for finding all prime numbers, not just Mersenne primes.
Mersenne primesĀ are a key target for prime hunters becauseĀ there is a particularly efficient way to test if a number of the form 2n ā 1 is prime or not, making it easier to search for massive prime numbers.
āItās a surprise that this discovery has happened so soon after the previous one,ā says Bethune. The previous largest prime was discovered towards the end of 2015, but was 5 million digits larger than the one before that was discovered in 2013, a gap five times larger than the difference between M77232917 and its predecessor. Itās not known how often Mersenne primes should occur, although there are some conjectures.
The recent discovery could mean that Mersenne primes arise more often than previously thought, or that there is a random clump closer together than expected. Increasing computing power and better software is also speeding up the process.
GIMPS will continue hunting for large Mersenne primes. The next major goal to find a prime 100 million digits long, which would net a $150,000 award administered by the Electronic Frontier Foundation.
