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Last Updated: Wednesday, 3 December, 2003, 01:32 GMT
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Prime position for large number
 By Dr David Whitehouse BBC News Online science editor

 If written down it would stretch 20 kilometres
A student has used his computer to find the largest prime number discovered so far.

Primes are important to encryption and could lead to uncrackable codes.

The new figure, identified by Michael Shafer, contains 6,320,430 digits, and would take someone the best part of five weeks to write out longhand.

Shafer was taking part in a mass computer project known as the Great Internet Mersenne Prime Search (Gimps).

The project spent 25,000 years of computer time to find the new prime number.

A prime is a number that can only be divided by one and itself.

Virtual supercomputer

Shafer, a chemical engineering graduate student at Michigan State University, said: "I had just finished a meeting with my advisor when I saw the computer had found the new prime.

"After a short victory dance, I called up my wife and friends involved with Gimps to share the great news."

 PRIME NUMBER GUIDE An integer greater than one is a prime if its only divisors are one and itself The first primes are 2, 3, 5, 7, 11, etc. 10 is not because it is divisible by 2 and 5 A Mersenne prime is a prime of the form 2^P-1 The first Mersenne primes are 3, 7, 31, 127, etc
Shafer used a 2 GHz Pentium 4 Dell Dimension PC running for 19 days to prove the number was prime.

"The software runs great without affecting the computer. I get my work done and contribute to the project at the same time."

Now in its eighth year, Gimps has accomplished six consecutive successes.

"Great teamwork has paid off for us again," says Gimps founder George Woltman.

"In addition to congratulating Michael Shafer, we wish to thank all 60,000 volunteer home users, students, schools, universities and businesses from around the world that contributed to this discovery.

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

Building blocks

Gimps pulls together hundreds of thousands of computers in parallel to create a virtual supercomputer running at nine trillion calculations per second.

This enabled Gimps to find the prime in just two years instead of the 25,000 years a single computer would have required.

Prime numbers have long fascinated mathematicians.

A whole number greater than one is 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 only 40 known Mersenne primes.

Their study has been central to number theory since they were first discussed by Euclid in 350 BC.

Big prizes

The man whose name they now bear, the French monk Marin Mersenne (1588-1648), made a prediction about which values of "P" would yield a prime.

It took 300 years and many important discoveries in mathematics to prove his conjecture.

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.

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 10-million-digit prime-number, a challenge Gimps participants are already working on.

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