Largest prime number discovered – with more than 23m digits

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This article titled “Largest prime number discovered – with more than 23m digits” was written by Ian Sample Science editor, for The Guardian on Thursday 4th January 2018 17.38 UTC

At more than 23m digits long, the number is something of a beast. But for mathematicians, the latest discovery from a global gang of enthusiasts is a thing of beauty: the largest prime number ever found.

Known simply as M77232917, the figure is arrived at by calculating two to the power of 77,232,917 and subtracting one, leaving a gargantuan string of 23,249,425 digits. The result is nearly one million digits longer than the previous record holder discovered in January 2016.

The number belongs to a rare group of so-called Mersenne prime numbers, named after the 17th century French monk Marin Mersenne. Like any prime number, a Mersenne prime is divisible only by itself and one, but is derived by multiplying twos together over and over before taking away one. The previous record-holding number was the 49th Mersenne prime ever found, making the new one the 50th.

“I’m very surprised it was found this quickly; we expected it to take longer,” said Chris Caldwell, a professor of mathematics who runs a website on the largest prime numbers at the University of Tennessee at Martin. “It’s like finding dead cats on the road. You don’t expect to find two so close to one another.”

The new prime number was originally found on Boxing Day by the Great Internet Mersenne Prime Search (Gimps) collaboration which harnesses the number-crunching power of volunteers’ computers all over the world. In the days after, four more computers sporting different hardware and software were set the task of verifying the discovery. Those computers confirmed the result, taking between 34 and 82 hours each.

To find M77232917 in the first place took six full days of nonstop computing on a PC owned by Jonathan Pace, a 51-year old electrical engineer from Germantown, Tennessee. It is the first prime that Pace’s computer has churned out in 14 years on the Gimps project. He is now eligible for a $3,000 award.

When asked about mathematicians’ fascination with such mammoth numbers, Caldwell said: “They are exciting to those of us who are interested in them. It’s like asking why do you climb a mountain.” He compares prime numbers to diamonds, with small ones finding uses in encryption and other applications, but large ones being more like showpieces. “That’s what we’re talking about here: it’s a museum piece as opposed to something that industry would use,” he said.

Curtis Cooper, a professor of mathematics at the University of Central Missouri, found the previous record-holding Mersenne prime in 2016, the fourth prime he has helped to find through the Gimps project in 20 years. He said he was a little sad at having lost the record so soon, but added: “I’m really happy for the whole organisation and the guy who found it. He’d been searching for 14 years, so he’s worked as hard as I have.”

“Discovering new primes, which are things you can touch, it’s the realisation of my love for mathematics. That’s the appeal for me,” he said.

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