How to discover your own prime number

  • 20 Jan 2016
The beginning of Mersenne prime M74207281
The beginning of Mersenne prime M74207281

This month, GIMPS, the Great Internet Mersenne Prime Search, announced the discovery of the largest known prime number: 2<sup>74,207,281</sup>-1. That's two, multiplied 74,207,281 times, with 1 subtracted from it.

The number was calculated in 31 days on a PC with a standard Intel Haswell Core i7-4790 consumer CPU, running GIMPS' Prime95 software. It's the 49th known Mersenne prime (a prime number that is one less than a power of two) and the third to be discovered by Curtis Cooper, a mathematician at the University of Central Missouri, who volunteered a university computer for the GIMPS project.

The number, dubbed M74207281, has 22,338,618 digits -- 5 million more than the previous longest prime. If you download a copy of the number, you get a 21.7MB text file.

The new prime has an official discovery date of 7 January 2016, but was actually reported to the GIMPS server by Dr Cooper's computer on 17 September 2015. A bug prevented a notification from being sent and the prime was only noticed during routine maintenance of the GIMPS database.

When a number 2<sup>n</sup>-1 is prime it is said to be a Mersenne prime, named after the French monk Marin Mersenne, who studied the numbers in the early 17th century. Founded in 1996, GIMPS is the longest running "grassroots supercomputing" project in Internet history and is responsible for the discovery of all 15 of the largest known Mersenne primes.

Although Cooper is a mathematician working on university equipment, anyone with a computer can try their hand at calculating primes. GIMPS currently offers a reward of $3,000 (£2,117) for every Mersenne Prime calculated, with a massive $50,000 (£35,320) bounty for the first prime discovered with at least 100,000,000 digits.

To have a go, first create a GIMPS user account, download Prime95 for Windows, Linux, Mac OS X or FreeBSD, install it and log in. While an account isn't strictly required, it's necessary if you want to check your performance statistics and link multiple computers to your ID.

The software only uses idle CPU cycles that aren't required by anything else you might be doing, so shouldn't get in the way of the day-to-day running of your PC. The latest version, Prime95 28.7, has been optimized for Intel's new AVX2 instruction set to get the best performance out of Intel Haswell processors.

Although prime numbers can have cryptographic uses, the vast size of M74207281 rules it out for that purpose. However, Prime95 is popularly used to benchmark and stress test computing hardware, and led to the discovery of a bug affecting Intel's new Skylake processors, which can cause system freezes when carrying out mathematically intensive computations. Motherboard BIOS patches are now being released to rectify the problem.