Largest Known Prime Number Found: Rare, With Over 23 Million Digits

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.