Biggest ever prime number found with 17 million digits

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The search from prime numbers is the mathematics equivalent of amateur gold mining, with unabashed enthusiasts pouring over their work for months on end; punctuating their diligent searches with rare moments of excitement.

It has, for example, been four years since anyone discovered a new prime number – or at least it was until Curtis Cooper, of the University of Central Missouri, hit the jackpot.

Cooper is part of a network of prime number hunters, known as the Great Internet Mersenne Prime Search, or Gimps for short. And as their names hints, this group aren't just interested in any old prime numbers, but a special form of prime number, known as Mersenne primes.

As elementary maths has taught us, prime numbers are those which can only be divided by themselves and 1. There are of course millions of prime numbers, but some of them form a pattern known as Mersenne Primes, which can be defined as Mp=2p-1. Both three and seven, therefore, are Mersenne primes (where p=2, or p=3).

Cooper's prime number is a little bigger – it is in fact 257,885,161–1; a 17 million digit number that took the university's computers 39 days to prove it really was a prime.

Prime numbers are hugely important for computer scientists, forming a central component of modern encryption. That said, encryption works by relying on big prime numbers, but it doesn't really require new ones to be found.

So the hunt for new, bigger primes is really done for pure intellectual satisfaction. Even so, the £3,000 prize from Gimps that Cooper has collected will probably help sweeten the discovery a little.

07 Feb 2013

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