# The world has a brand new largest prime number

20 Jan 2016

The largest known prime number ever has been discovered by researchers in Missouri, with the number comprising of more than 22m digits.

Prime numbers – three, five, seven etc – are divisible only by themselves and one, and play an important role in computing and encryption.

Named after a 17th-century monk who took an interest in seeking out prime numbers, Mersenne prime numbers are those that are factored by two, minus one, meaning a 2p -1 equation.

Therefore, the first Mersenne primes are 3, 7, 31, and 127 corresponding to P = 2, 3, 5, and 7 respectively. There were only 48 known Mersenne primes prior to the latest discovery.

The new prime number is written as 2^74,207,281-1 – which denotes its two multiplied by itself 74,207,281 times, minus one,

## Seasoned detective

The pursuit of prime numbers seems odd but, with the help of GIMPS – the Great Internet Mersenne Prime Search project – discoverers are in line for \$3,000 if they find a new one.

A seasoned mathematical detective, University of Missouri’s Dr Curtis Cooper’s computer was the machine that did most of the work on this latest finding, his fourth such discovery since the GIMPS project started back in 1996.

Cooper’s discovery was actually back in September but a computer glitch meant his email, listing the number, was never sent. In a turn of fortune, some machine maintenance found the original recording and now, dated 17 September 2015, Cooper has made history again.

“The search for more Mersenne primes is already under way,” said the organisers behind GIMPS. “There may be smaller, as yet undiscovered Mersenne primes, and there almost certainly are larger Mersenne primes waiting to be found.”

## Encryption keys

Why should we care about these numbers? Well, modern cryptography is heavily reliant on prime numbers, thanks to the difficulty in factoring extremely large numbers back down to primes.

According to Geek.com, that fact makes primes “vitally important to communications”.

“Most modern computer cryptography works by using the prime factors of large numbers,” explained Geek.com’s Graham Templeton.

“The large number that was used to encrypt a file can be publicly known and available, because the encryption works so only the prime factors of that large number can be used to decrypt it again.

“Though finding those factors is technically only a matter of time, it’s a matter of so much time that we say it cannot be done. A modern supercomputer could chew on a 256-bit factorisation problem for longer than the current age of the universe, and still not get the answer.”

Although Cooper’s computer did the leg work, the person who logs the result takes the prize.

Main image via Shutterstock

Gordon Hunt was a journalist with Silicon Republic

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