The World Has A New Largest-Known Prime Number

December 21, 2018

There’s a new behemoth in the ongoing search for ever-larger prime numbers — and it’s nearly 25 million digits long.

A prime is a number that can be divided only by two other whole numbers: itself and 1. The newly discovered number is what’s known as a Mersenne prime, named for a French monk named Marin Mersenne who studied primes some 350 years ago.

Mersenne primes have a simple formula: 2n-1. In this case, “n” is equal to 82,589,933, which is itself a prime number. If you do the math, the new largest-known prime is a whopping 24,862,048 digits long.

We would write the number out for you, but it would fill up thousands of pages, give or take, and look like this gigantic zip file.

The latest Mersenne prime comes courtesy of a project started in 1996 called the Great Internet Mersenne Prime Search, in which people download special software that runs in the background on their computers. A computer owned by Patrick Laroche of Ocala, Fla., discovered the number on Dec. 7, and mathematicians have spent the past two weeks verifying the calculations. It’s more than a million and a half digits longer than the previous largest known prime, discovered about a year ago by a computer in Germantown, Tenn.

Why should you care about Mersenne primes? They’ve proven useful in generating reasonably random numbers, but the best answer might be simply because they’re there — and they’re majestic.

Chris Caldwell, a mathematician at the University of Tennessee, Martin, talked to NPR in 2009 about these large primes.

“Mersennes, in a way, are kind of like a large diamond,” Caldwell said back in 2009. Think about the Hope Diamond, a 45.52-carat diamond that sits in a special case in the Smithsonian National Museum of Natural History, usually with crowds around it.

“Nobody there looking at the Hope Diamond ever asks, ‘Why did they bother to dig it up?’ or ‘What is it good for?’ — even though it really isn’t good for much other than to just hang there and people to look at,” Caldwell said. “And in many ways, the Mersennes play that same role — that they really are the jewels of number theory.”

Copyright 2018 NPR. To see more, visit https://www.npr.org.

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