Mathematicians have discovered the largest prime number yet – two to the power of 257,885,161, minus one.
The number has 17,425,170 digits, and was found using the Great Internet Mersenne Prime Search (GIMPS) project – the longest-evercontinuously-running global ‘grassroots supercomputing’ project, involving 360,000 CPUs peaking at 150 trillion calculations per second.
The new prime number is a member of a special class of extremely rare prime numbers known as Mersenne primes, and is only the 48th of these to be discovered.
Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. All take the form 2 to the power of p – 1, where p is also a prime number – although not all numbers that take that form are prime.
Mathematicians suspect that there may be an infinite number of Mersenne primes. GIMPS, founded in 1996, has discovered all 14 of the largest known Mersenne primes – with this latest one taking 39 days of non-stop computing to establish.
To prove there were no errors in the prime discovery process, the latest one was independently verified using different programs running on different hardware.
This is the third record prime for Dr Curtis Cooper and the University of Central Missouri, the others having been discovered in 2005 and2006. Computers at UCLA broke that record in 2008 with a 12,978,189 digit prime number that was the longest until now.
Work to find more will continue – especially given the $150,000 reward promised by the Electronic Frontier Foundation to the first person to find a 100 million-digit prime.
Anyone with a reasonably powerful PC can join GIMPS and have a shot themselves, with the necessary software available free at www.mersenne.org/freesoft.htm.