# Missouri Mathematicians Discover New Prime Number

## At more than 22 million digits, it’s the longest prime yet

smithsonian.com

A group of mathematicians at the University of Central Missouri have just discovered a new prime number, and at more than 22 million digits, it’s the longest one yet.

People have been hunting for prime numbers for thousands of years, ever since the concept was first discovered by ancient Greek mathematicians around 500 BCE. Prime numbers, of course, are curious in that they are only divisible by one and themselves. This newest prime belongs to a category called Mersenne Primes, named after a 16th century French monk and mathematician.

The formula used to find these primes is 2n-1, which is relatively simple – just repeat until you find a number that can only be divided by one and itself. It’s a pretty easy calculation to make, but because not every number it comes up with is a prime, researchers rely on computers to help them sort through the increasingly long numbers in the search for larger and larger primes, Darren Orf writes for Gizmodo.

After 31 days of non-stop calculations, a computer program created by the Great Internet Mersenne Prime Search project (GIMPS) uncovered the newest prime number on September 17, 2015, but thanks to a glitch in the reporting system, it took until January 7 for the researchers to discover it in their database.

“There was some embarrassment there that we went four months here without discovering it,” lead researcher Curtis Cooper tells Matt Parker in a video for Stand-Up Maths. According to Cooper, one of his colleagues was performing routine maintenance on their GIMPS server when he came across the enormous number. After running it through some tests, he realized that they had discovered a new prime number.

M74207281, as mathematicians are calling the new prime, is 5 million digits longer than the previous record holder, which was also discovered by the GIMPS program. The new prime is too long to write out in full here, but it was found by multiplying 2 by itself 74,207,281 times, and then subtracting one. Because the calculations used to find Mersenne Primes are so simple, Cooper and his team don’t even need a specialized supercomputer to run the GIMPS software, James Vincent reports for The Verge.

M74207281's impressive length makes it a bit unwieldy to use for things like computer encryption. However, hunting for enormous primes like this can help pinpoint errors in computer systems that could be used to get around security measures, the BBC reports. The number also has symbolic value and demonstrates that their software is capable of uncovering new primes, even as they get longer and longer.

"One prime project discovered that there was a problem in some computer processors that only showed up in certain circumstances," University College London cybersecurity expert Steven Murdoch tells the BBC.

M74207281 may not be good for much on its own, but its discovery does come with a cool \$3,000 award for Cooper and his team. Even so, that amount pales before the \$150,000 award GIMPS is offering for its next major goal: discovering a prime number with 100 million digits.