An electrical engineer in Germantown, Tennessee, has been searching for big prime numbers for the last 14 years, as a volunteer who uses his computer to run a software designed to do exactly that. In late December, Jonathan Pace, 51, struck gold when his machine pumped out the largest known prime number yet.

What is this number? Well, since it clocks in at a humongous 23 million digits long, writing it down in its entirety, five digits to an inch, would require over 73 miles of space. And at the speed of five digits written every second, writing the number out would take 54 days, without any breaks. So no, that number itself won’t be written out in full here.

However, it is the result you get if you multiply the number 2 by itself 77,232,917 times, and then subtract 1 from it. So that you don’t have to go through the process of verifying it for yourself, an online collaboration called Great Internet Mersenne Prime Search (GIMPS) — whose software Pace was running — already did that.

The number was discovered Dec. 26, but GIMPS made the announcement Wednesday, having spent the intervening time running “four different programs on four different hardware configurations” to confirm proof of primality.

The newly discovered number has exactly 23,249,425 digits and is called M77232917, since it also belongs to a rare class of prime numbers called Mersenne primes. These numbers are always 1 short of a multiplication of 2s. For instance, the first Mersenne prime is 3 (2x2-1), the next is 7 (2x2x2-1), after that is 31 (2x2x2x2x2-1) and so on.

The new addition to the Mersenne primes is the 50th number of its kind to have been found, and it beat the previous largest known prime number, also a Mersenne prime, by 910,807 digits. That number was also found by the GIMPS collaboration, in January 2016. In terms of writing it down, the 49th Mersenne prime would be about 3 miles shorter than its successor.

Mersenne primes are named in honor of Marin Mersenne, a French friar who studied them almost four centuries ago.

For his efforts, Pace won a $3,000 GIMPS research discovery award. If you would like to have a chance of winning another such award in the future, you can volunteer with GIMPS by installing its free software on your computer and running it in the hope of finding the next Mersenne prime. The program can be downloaded using this link.

GIMPS hopes to win the $150,000 award, announced by the Electronic Frontier Foundation, for discovering the first prime number with over 100 million digits. There is also a $250,000 award for finding the first billion-digit prime number.

Really big prime numbers don’t have many practical uses yet, but cryptography algorithms based on prime numbers have been developed.</s>Maths fans can’t get enough of numbers that are millions of digits long and can only be divided by themselves and one. Now, through a collaborative effort, utilising computers distributed around the world, they’ve discovered that the number 277,232,917 – 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, 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</s>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.</s>Jonathan is one of thousands of volunteers using free GIMPS software.

The new prime number, also known as M77232917, is calculated by multiplying together 77,232,917 twos, and then subtracting one. It is nearly one million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 50th known Mersenne prime ever discovered, each increasingly difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 16 Mersenne primes. Volunteers download a free program to search for these primes, with a cash award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell maintains an authoritative web site on the largest known primes, and has an excellent history of Mersenne primes.

The primality proof took six days of non-stop computing on a PC with an Intel i5-6600 CPU. To prove there were no errors in the prime discovery process, the new prime was independently verified using four different programs on four different hardware configurations.
• Aaron Blosser verified it using Prime95 on an Intel Xeon server in 37 hours.
• David Stanfill verified it using gpuOwL on an AMD RX Vega 64 GPU in 34 hours.
• Andreas Höglund verified the prime using CUDALucas running on NVidia Titan Black GPU in 73 hours.
• Ernst Mayer also verified it using his own program Mlucas on 32-core Xeon server in 82 hours. Andreas Höglund also confirmed using Mlucas running on an Amazon AWS instance in 65 hours.

Jonathan Pace is a 51-year old Electrical Engineer living in Germantown, Tennessee. Perseverance has finally paid off for Jon—he has been hunting for big primes with GIMPS for over 14 years. The discovery is eligible for a $3,000 GIMPS research discovery award.

GIMPS Prime95 client software was developed by founder George Woltman. Scott Kurowski wrote the PrimeNet system software that coordinates GIMPS' computers. Aaron Blosser is now the system administrator, upgrading and maintaining PrimeNet as needed. Volunteers have a chance to earn research discovery awards of $3,000 or $50,000 if their computer discovers a new Mersenne prime. GIMPS' next major goal is to win the $150,000 award administered by the Electronic Frontier Foundation offered for finding a 100 million digit prime number.

Credit for this prime goes not only to Jonathan Pace for running the Prime95 software, Woltman for writing the software, Kurowski and Blosser for their work on the Primenet server, but also the thousands of GIMPS volunteers that sifted through millions of non-prime candidates. In recognition of all the above people, official credit for this discovery goes to "J. Pace, G. Woltman, S. Kurowski, A. Blosser, et al."
The Great Internet Mersenne Prime Search announces the discovery of the latest largest known prime number, a Mersenne prime with 23,249,425 digits equal to 277,232,917 − 1.