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Wednesday, 5 December, 2001, 11:42 GMT
Number takes prime position
By BBC News Online science editor Dr David Whitehouse

The largest prime number yet discovered has just been revealed to the world.

 There are more primes out there George Woltman, Gimps founder
The new number, expressed as 213,466,917-1, contains 4,053,946 digits and would take the best part of three weeks to write out longhand.

The prime number - a number that can only be divided by one and itself - was discovered by Michael Cameron, a 20-year-old Canadian participant in a mass computer project known as the Great Internet Mersenne Prime Search (Gimps).

Mersenne primes are important for the theory of numbers and they may help in developing unbreakable codes and message encryptions.

The Gimps project spent 13,000 years of computer time to find the new prime number.

Big effort

Cameron used an 800 MHz AMD T-Bird PC, running part-time for 45 days to find the number.

 Prime numbers An integer greater than one is called a prime number if its only divisors are one and itself The first prime numbers are 2, 3, 5, 7, 11, etc. For example, the number 10 is not prime because it is divisible by 2 and 5 A Mersenne prime is a prime of the form 2P-1 The first Mersenne primes are 3, 7, 31, 127, etc
"A friend informed me that if I was going to leave my computer on all the time I should make use of that wasted CPU time," he said. "I put Gimps on my PC because it does not interfere with my work on the computer. Finding the new prime was a wonderful surprise.

Gimps founder, George Woltman, said: "Finding this prime is by far our most impressive accomplishment to date, having taken two years of non-stop work.

"In addition to congratulating Michael Cameron, we wish to thank all 130,000 volunteer home users, students, schools, universities and businesses from around the world that contributed to Gimps."

Theory of numbers

Prime numbers have long fascinated mathematicians. A whole number greater than one is called a prime if its only divisors are one and itself. They are important for number theory. The Fundamental Theory of Arithmetic says that primes are the building blocks of numbers.

The first prime numbers are 2, 3, 5, 7, 11. A Mersenne prime is a prime number of the form 2P-1 (where the superscript "P" is the exponent, or number of times the original figure must be multiplied by itself). The first Mersenne primes are 3, 7, 31, 127. There are now only 39 known Mersenne primes.

The study of Mersenne primes has been central to number theory since they were first discussed by Euclid in 350 BC. The man whose name they now bear, the French monk Marin Mersenne (1588-1648), made a famous prediction about which values of "P" would yield a prime. It took 300 years and many important discoveries in mathematics to prove his conjecture.

The new Mersenne prime has been independently verified using three weeks of computer time on a 667 MHz Alpha workstation. It is the fifth, record prime found by the Gimps project, and the third discovered using a computing grid developed by Entropia.

All corners

Gimps was formed in January 1996 by George Woltman, to discover new world-record-sized Mersenne primes. All the necessary software can be downloaded for free. Most Gimps members join the search for the thrill of possibly discovering a record-setting, rare, and historic, new Mersenne prime.

 It's great seeing such a repeatedly successful research effort having volunteers provide hundreds of thousand of PCs from virtually every time zone of the world Scott Kurowsk, Entropia founder
Previous Gimps Mersenne prime discoveries were made by members in various countries.

In June 1999, Nayan Hajratwala discovered the previous largest-known prime number in the US. In January 1998, Roland Clarkson discovered the 37th Mersenne prime, also in the US; Gordon Spence discovered the 36th in August, 1997, in the UK; Joel Armengaud discovered the 35th in November, 1996, in France.

The exercise in mass-distributed computing that found the new prime would have been much more costly without the distributed computing power harnessed by Entropia's PrimeNet system.

Money reward

"Entropia is delighted to have a role in this discovery," its founder, Scott Kurowski, told BBC News Online.

"It's great seeing such a repeatedly successful research effort having volunteers provide hundreds of thousand of PCs from virtually every time zone of the world. George runs an amazing and fun project."

In May 2000, a Gimps participant received a \$50,000 co-operative computing award from the Electronic Frontier Foundation for the discovery of the first million-digit prime number. A \$100,000 award awaits discovery of a ten-million-digit prime number, a challenge Gimps participants are already working on.

"There are more primes out there," said George Woltman, "and anyone with an internet-connected computer can participate."

"Joining Gimps is a great way to learn about math through participation - plus you might find a new Mersenne prime, like Michael," he said.