The world’s largest prime number has 17million digits

The record for the world’s largest prime number has been broken – by over four million digits.

The number – 2 to the power of 57,885,161 minus 1 – is 17,425,170 numerals long and if you spent 12 hours a day writing it out at the rate of one digit a second it would take 403 days to complete.

A prime number is only divisible by itself and 1, with the first ones being 2, 3, 5, 7 and 11. Although of little significance, they have long fascinated amateur and professionals and the discovery of a new one is a badge of honour in mathematical circles.

Although there are an infinite amount of prime numbers, the hunt for the largest has in recent years centred on rare Mersenne primes, named after Marin Mersenne, a 17th-century French monk and mathematician.

Mersenne primes are 2 to the power of p minus 1, in which p is also a prime number and the latest is only the 48th to be found.

‘It’s sort of like finding a diamond,’ Chris Caldwell, of the University of Tennessee, told the New Scientist. ‘People like these large primes and so they have a value.’

The number was found with the Great Internet Mersenne Prime Search, a network that harnesses the spare power of 360,000 computers around the world.

If you wanted to print out the new number, it would eat up 5,319 pages of A4 if you used the Courier New font at 11-point.

In 300BC the Greek mathematician Euclid is thought to have published the first proof of the theory that prime numbers are infinite.

The man behind the discovery is Curtis Cooper, which makes a hat trick for him: he also found two earlier highest prime numbers.

The previous record was held by a prime number that is a mere 12,978,189 digits long. The icing on the cake is that this discovery is also a very rare Mersenne prime - the 48th, in fact.

The find breaks a long dry spell: it has been four years since the last biggest ever prime number was found.

Of all the numbers between 2 25,964,951-1 just 1,622,441 are prime, and of those, only 42 are Mersenne primes.

Prime numbers have little value in themselves to mathematicians, but they are nonetheless prized as oddities that are difficult to find.

Says Chris Caldwell at the University of Tennessee: 'It's sort of like finding a diamond.

'For some reason people decide they're like diamonds and so they have a value.'

This latest giant prime number was found as part of the Great Internet Mersenne Prime Search (GIMPS), a project that uses spare processing power on thousands of volunteer computers to look for and calculate prime numbers.

Dr Cooper's computer took 39 days of flat-out computing to verify that this number was indeed a prime.

He had crunched the number as a result of running the GIMPS software on 1,000 computers at the university.

Dr Cooper's find was verified by other powerful computers running different software.

Anyone can download the software and put their own computer to work on finding ever bigger primes from www.mersenne.org, which announced the finding.

And if you're fired up by the hunt, the Electronic Frontier Foundation is offering a prize \$150,000 to the person who discovers the first 100 million-digit prime.