Science

# FedEx employee from Tennessee discovers largest known prime number

Key Points
• The world's largest known prime number, with 23 million digits, was discovered by a volunteer for a prime-number hunting project.
• The Mersenne primes have been discussed by mathematicians since at least Euclid.
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FedEx employee from Tennessee discovers largest known prime number. It's 23 million digits long

A FedEx employee from Tennessee has made mathematical history with the discovery of the largest known prime number.

Jonathan Pace, a 51-year-old engineer living in Germantown, Tennessee, discovered the number after running a special piece of computational software for six days straight. Pace is a volunteer for a project called the Great Internet Mersenne Prime Search (GIMPS). Thousands, armed with "reasonably modern" computers and GIMPS software, volunteer on the project, according to the GIMPS website.

The number, called M77232917, is the 50th "Mersenne prime" to be discovered.

Mersenne primes are a group of prime numbers named for the French monk Marin Mersenne, who studied the numbers more than three centuries ago. The number is more than 23 million digits long — 1 million digits longer than the 49th known Mersenne prime, discovered in January 2016.

It is calculated by raising the number 2 to the 77,232,917th power and then subtracting 1.

This is Pace's first discovery since he began volunteering for the GIMPS project 14 years ago.

These primes are exceedingly rare and sporadic, said Chris Caldwell, a professor of mathematics and statistics at the University of Tennessee at Martin, who studies prime numbers and has written a history of the Mersenne primes.

There are, after all, only 50 Mersenne primes among all the numbers that run up to 23 million digits. But it is easier to prove the Mersenne numbers are primes than it is to prove other primes, he said.

Prime numbers have been an interest of mathematicians for more than 2,000 years.

"Finding a prime is not going to change any theorems in mathematics, but this is a type of prime that has been interesting to mathematicians since several centuries before Christ," Caldwell said. Even the ancient Greek mathematician Euclid talked about what would later become the Mersenne primes, he said.

Caldwell added that the discovery was akin to breaking a land speed record.

The last few Mersenne primes have been closer to each other than the researchers expected, he said.

The numbers seem to occur sporadically because researchers don't fully understand the pattern they follow, he said. "So you expect in any process that appears random to have some close groupings of numbers. But we didn't expect to find another one so soon after the last one."

"In the long run, we hope to use these data to predict how often these occur," he added.

Since its founding in 1996, GIMPS has discovered the last 16 Mersenne primes. The software GIMPS uses is complex enough that it has even been able to detect bugs in Intel processors that would rarely have been encountered by normal users.

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