Project discovers Mersenne prime of 22 million digits

A university computer run by Curtis Cooper has discovered the forty-ninth Mersenne prime. The number 274,207,281-1 consists of 22,338,618 digits. The new prime is nearly five million digits larger than the previous largest prime.

A Mersenne prime is a prime that is exactly one less than the power of two, or 2n – 1. The first four n numbers to form the first four Mersenne primes are 2, 3, 5, 7 where respectively 3 , 7, 31 and 127. The new number discovered using software from the Great Internet Mersenne Prime Search project is also the new largest prime number known. This is the fourth time that Curtis Cooper has found a Mersenne prime using a university computer at the University of Central Missouri in the United States. He found the other three primes in 2005, 2006 and 2013. It is not known whether there is another prime between the 44th and 49th Mersenne prime. For example, the 29th number was discovered after the discovery of the 30th and 31st.

The new Mersenne prime was already discovered on September 17, 2015, but nobody noticed it before January 7, 2016. Getting the number took 31 days of non-stop computing on a PC with an Intel i7-4790 CPU. To verify that the number is correct, two others ran the calculation again using Nvidia Titan Black GPUs with CudaLucas software. in that case it took ‘only’ 2.3 days to verify the number. With an AMD Fury X GPU with ClLucas it took 3.5 days. Another verification was done with MLucas software on two 18-core Intel Xeons on an Amazon EC2 server in 3.5 days. Recently, another bug in Intel Skylake processors was revealed by running the Prime95 program when the number 14942209 is tested. Prime95 is from the Mersenne Resarch Group and is used in the Gimps project.

Gimps is offering a $3,000 reward for the find. A goal of Gimps is to find a Mersenne prime number of more than 100 million digits. The Electronic Frontier Foundation has made $150,000 available for this.