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Last Updated: Monday, 7 June, 2004, 11:55 GMT 12:55 UK
Largest Prime Number discovered
By Dr David Whitehouse
BBC News Online science editor

The biggest prime number yet found
If written down it would stretch 25km
A scientist has used his computer to find the largest prime number found so far - written out, it would stretch for 25 kilometres.

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

The new figure, identified by Josh Findley, contains 7,235,733 digits, and would take someone the best part of six weeks to write out longhand.

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

Rare number

He is a volunteer in the Mersenne.org research project called the Great Internet Mersenne Prime Search (Gimps). Mr Findley used his home computer and free software as part of an international grid of 240,000 networked computers.

The new number, expressed as 2 to the 24,036,583th power minus 1, has 7,235,733 decimal digits. It is nearly a million digits larger than the previous largest known prime number, and belongs to a special class of rare prime numbers called Mersenne primes.

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
It is only the 41st known Mersenne prime, named after Marin Mersenne , a 17th Century French monk who first studied the rare numbers 300 years ago.

Mersenne primes are most relevant to number theory, but most participants join Gimps for the fun of having a role in real research - and the chance of finding a new Mersenne prime.

Gimps is closing in on the $100,000 Electronic Frontier Foundation award for the first 10-million-digit prime.

"An award-winning prime could be mere weeks or as much as a few years away - that's the fun of math discoveries," said Gimps founder George Woltman.

The Gimps participant who discovers the prime will receive $50,000. Charity will get $25,000. The rest will be used primarily to fund more prime discoveries. In May 2000, a previous participant won the foundation's $50,000 award for discovering the first million-digit prime.

Findley, a consultant to the US National Oceanic and Atmospheric Administration in La Jolla, California, says: "I'm still surprised at the discovery. Even after five years running Gimps on my computers, I didn't expect to find a new Mersenne prime."

He used a 2.4 GHz Pentium 4 Windows XP computer running for 14 days to prove the number was prime.

"There are more primes out there," says Woltman, "and anyone with an Internet-connected computer can participate."

Hidden computer problems

Prime numbers have long fascinated mathematicians. 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.

The number 10 is not prime because it is divisible by 2 and 5.

Mersenne primes have been central to number theory since they were first discussed by Euclid in 350 BC.

The Fundamental Theory of Arithmetic says they are the building blocks of numbers.

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.

A Mersenne prime is a prime of the form 2^P-1. The first Mersenne primes are 3, 7, 31, 127, etc. There are only 42 known Mersenne primes.

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

Historically, searching for Mersenne primes has been used as a test for computer hardware. The free Gimps program used by Findley has identified hidden hardware problems in many computers.

Mathematicians crack big puzzle
19 Nov 99  |  Science/Nature
Number takes prime position
05 Dec 01  |  Science/Nature
The secret of squares revealed
03 Mar 00  |  Science/Nature

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