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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.
The prime number  a number that can only be divided by one and itself  was discovered by Michael Cameron, a 20yearold 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 TBird PC, running parttime for 45 days to find the number.
Gimps founder, George Woltman, said: "Finding this prime is by far our most impressive accomplishment to date, having taken two years of nonstop 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 2^{P}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 (15881648), 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 worldrecordsized Mersenne primes. All the necessary software can be downloaded for free. Most Gimps members join the search for the thrill of possibly discovering a recordsetting, rare, and historic, new Mersenne prime.
In June 1999, Nayan Hajratwala discovered the previous largestknown 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 massdistributed 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 cooperative computing award from the Electronic Frontier Foundation for the discovery of the first milliondigit prime number. A $100,000 award awaits discovery of a tenmilliondigit prime number, a challenge Gimps participants are already working on. "There are more primes out there," said George Woltman, "and anyone with an internetconnected 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.

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