News from the world of maths: Prime record broken?

Monday, September 08, 2008

Prime record broken?

Volunteers have claimed to have found the largest prime number yet — twice within a fortnight! The two new record breakers are both Mersenne primes: numbers which can be written in the form 2p-1, where p is also prime.

Every whole number can be written as a product of prime numbers in a unique way, and this is why the primes are regarded as the building blocks of number theory. Mathematicians have known since antiquity that there are infinitely many primes, but there isn't a formula which describes them all. To check if a number is prime, you have to go through painstaking algorithms that take up a huge amount of computing power. The task becomes easier when the number you're checking for primeness is a Mersenne number of the form described above.

But still, one computer isn't enough to do the job: the eleven previous largest prime discoverers have all been part of the Great Internet Mersenne Prime Search (GIMPS), which uses the computing power "donated" by tens of thousands of volunteers to chomp through the necessary calculations. The previous record prime — found in September 2006 — would have taken an ordinary PC 4000 years to find, but with the help of a 70,000 strong computer network, able to perform 22 trillion calculations per second, popped out in "only" nine months.

Why would anyone want to find the largest prime to date? For the fun of it, of course, in true nerdy-style, but there's the added bonus of a $50,000 prize for the first to discover a prime with 10 million digits. On a less frivolous level, primes are extremely useful in cryptography: because factorising large numbers into their prime factors is so computationally expensive, these factors can, and do, serve as almost unbreakable keys to encrypted messages — like the ones we send over the Internet every time we use our credit cards or send encrypted emails.

Experts are now performing independent checks to verify that the two new numbers really are prime, and are due to report back soon.

To find out more about GIMPS, previous Mersenne prime discoveries, and the role of primes in cryptography, read the Plus articles

posted by Plus @ 4:13 PM