# Prime time for PCs

How would you like to win $100,000 (pound;54,000) for your school? That is the prize being offered for the discovery of a prime number with more than 10 million digits. Primes are numbers which cannot be factorised.

They are the most important numbers in maths because every other number can be built by multiplying together a combination of these indivisible numbers.

Prime numbers are the atoms of arithmetic, but understanding these numbers is one of the greatest mathematical mysteries.

Maths is the science of patterns. Mathematicians spend their lives trying to find logic and order in the chaos that surrounds us. But when you look at a list of primes, it is extremely difficult to discern any rhyme or reason as to how nature chose these numbers. 2, 3, 5, 7, 11, 13, 17, 19I As one counts further through the universe of numbers it is increasingly difficult to predict where you'll find the next prime. You would have no difficulty finding an odd number with 10 million digits. But the sequence of primes is so wild that no one knows where to look for the next one.

Can we even be sure that there is such a big prime number? In one of the first great theorems of maths, the ancient Greek Euclid proved that the primes never run out but go on forever. So, thanks to Euclid we know there is a prize-winning prime out there to be discovered. The trouble is that Euclid's proof is no help in identifying where to find it. Prime numbers seem as randomly distributed as stars in the night sky.

Those who stare at the stars have in fact inspired modern mathematicians in their search for these elusive primes. Amateur stargazers have been enlisted by professional astronomers to scour the cosmos for new supernova activity.

Using the internet to share the load, each person gets a different patch of the night sky to analyse. Mathematicians realised that the same approach could be used for primes. Instead of the night sky, you get your own piece of the universe of numbers to comb for primes. Most people's computers are sitting idle most of the time. Why not get the combined forces of the world's desktop computers looking for big primes on their downtime?

Posted on the internet is a piece of software that can be downloaded on to your computer and when the machine isn't doing anything else, it hunts for primes. So far the project has delivered eight record-breaking primes. The first prime to cross the 1-million digit barrier earned a prize of $50,000 dollars. The prize money is being offered by the Electronic Frontier Foundation, a California-based organisation which is encouraging collaboration and co-operation in cyber-space. Earlier this year the record was broken again by a doctor in Germany. So obsessed had he become with the project that he had 24 PCs at home looking for primes. His record number has more than 7.8 million digits. The number is so huge that it would take more than six weeks to read it out aloud. But everyone's sights are now set on clearing the 10-million digit hurdle.

Prime numbers might seem a rather esoteric passion. But these indivisible numbers are now central to the codes that protect electronic secrets on the internet. Every time someone sends their credit card details across the internet, the card number is kept secure from prying eyes by the power of prime numbers. So a complete understanding of the primes might not only win you a prize of $100,000 dollars, but could in the wrong hands allow a hacker to get access to the world's credit card numbers.

Maybe we shouldn't be encouraging pupils to become criminal masterminds, but the prize money might help motivate more pupils to get into maths. So why not get all those school computers that are sitting idle during break and the lunch hour searching for that elusive 10-million digit number and perhaps it could be your school making the headlines with the next record-breaking prime.

Marcus du Sautoy is a professor of maths at Oxford and senior media fellow of the Engineering and Physical Sciences Research Council. He presents The Music of the Primes on BBC4 on September 28. To join the search for primes visit www.mersenne.orgprime.htm

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