Hunting for gigantic prime numbers

13th May 2005 at 01:00
Newspapers and radio stations were buzzing recently with the news of a new mathematical discovery: a record-breaking prime number had been discovered with a staggering 7.8 million digits.

Primes are numbers which cannot be divided by any smaller number except 1.

It is easy to check that a number like 17 is prime, but to check the indivisibility of a number with 7.8 million digits is an impressive feat.

Simply to read the prime number out aloud would take a month and half.

Perhaps the most amazing thing about the discovery, though, is that it wasn't found by some clever mathematician or by some huge mega-computer, but by an eye doctor in Germany.

Dr Martin Nowak found his record-breaking prime with the help of his desktop computer and a cunning piece of software downloaded from the internet. Six years ago he joined a band of amateur mathematical sleuths who are using the internet to co-ordinate a search for these elusive numbers.

The idea is to exploit the billions of computers around the world on people's desks that are sitting idly doing nothing most of the time. The software uses the potential of this huge parallel processing machine connected via the internet to hunt for primes while the computer is inactive.

By the end of the project Dr Nowak had 24 computers at home hunting for primes. Amateur astronomers have used a similar strategy in their search for new supernovas.

The huge portfolio of images of the night sky generated by professional telescopes are shared among participants' computers. Software downloaded from the internet then scours the image for the tell-tale signs of imminent supernova activity.

In the prime number quest, members of the team get their own bit of the universe of numbers to check for a new prime. So Dr Nowak's computer just struck lucky with its bit of the mathematical sky to look at. His number is in fact a special one called a Mersenne prime. Named after a 17th-century French monk, these primes are built by raising 2 to some power and then subtracting 1 from the answer. For example, 7 is a Mersenne prime because it is 23 - 1 = 2 x 2 x 2 - 1. But this doesn't always guarantee you a prime. For example, 24 - 1 = 15. Therein lies the mystery: which powers of 2 will get you a prime?

These numbers become huge very quickly. The explosive effect of powers of 2 is illustrated by the inventor of chess, who asked as payment for his creation one grain of rice on the first square of the chess board, two on the second, four on the third, eight on the next, etc. What the Indian king who offered the reward didn't realise is that by the 64th square of the board, he would need more grains of rice than the world's total rice production in the last century.

But is the discovery of such a gigantic prime exciting news for the mathematical community? Well, yes and no. Like Ellen MacArthur breaking the round-the-world sailing record, there is something momentous about each new prime number breakthrough. On the other hand, the ancient Greeks proved 2,000 years ago that the primes never run out. (You can see my football team Recreativo FC explain why there is an infinite number of primes in a short three-minute film at http:www.spiked-online.comsectionssciencesciencesurveyfilms.stm One should not underestimate the potential of the Great Internet Mersenne Prime Search (Gimps) to draw students into these deeper questions of mathematics. A prize of $100,000 (pound;53,000) awaits the first person to find a prime with more than 10 million digits.

Getting a school's computers joining the hunt for the next record prime might just help to solve all those financial problems.

Marcus du Sautoy is a professor of mathematics at Oxford university and an EPSRC senior media fellow. To join the Great Internet Mersenne Prime Search see: www.mersenne.orgMore resources can be found at

Maths subject focus, Teacher magazine, 22

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