Grid Discovers Largest Known Prime Number

Using an international grid of about 70,000 computers, researchers this month discovered a 9.1 million-digit figure.
Posted December 28, 2005

Sharon Gaudin

Using an international grid of about 70,000 computers, researchers this month discovered the largest known prime number.

The number, which is expressed as 2 to the 30,402,457th power minus 1, is a 9.1 million-digit figure. It was discovered by a team of researchers at Central Missouri State University.

''Working alone, it would take a brand new Pentium 4 computer about 4,500 years to find this number,'' says George Woltman, a retired computer programmer and founder of the Great Internet Mersenne Prime Search (GIMPS). ''It took all 70,000 computers 10 months to make this find. Each computer on the grid tests a different number and, depending on the speed of the computer, it takes about two weeks to a few months.''

Mersenne primes have, in many cases, been found by individuals, but this time the result came from a team that so far has contributed more processing time than any others -- the equivalent of 67,000 years running a 90MHz Pentium computer, according to GIMPS records. The Central Missouri State University team, led by professors Curtis Cooper and Steven Boone, used GIMPS software that ran on and off for about 50 days.

The new prime was independently verified in five days by Tony Reix of Bull S.A. in Grenoble, France.

The find is part of a special class of prime numbers called Mersenne primes. They are named after Marin Mersenne, a 17th century French monk who first studied the rare numbers 300 years ago, though Euclid first conjectured about them in 350 B.C. The latest number actually is the 43rd Mersenne Prime to be discovered.

It's difficult to understand the sheer size of this number.

''If you typed one number on a keyboard every second, it would take you 106 days to type out the whole number,'' Woltman told . ''This one number would have enough digits to fill up close to three Bibles.''

At this point, though, Woltman says there is no practical use for such a large number. ''It's kind of like climbing Mt. Everest. You climb it because it's there,'' he adds. ''It's a pure research project.''

Woltman launched the Great Internet Mersenne Prime Search back in early 1996 as a collective effort to find larger and larger prime numbers. Since then the group has had a virtual lock on the search. This month's discovery outweighs the last find -- a 7.8 million-digit prime that GIMPS found this past February.

Woltman says the group's series of finds demonstrates the power of the grid. ''We've been running our grid for about 10 years and we've had nine finds. It shows that a grid can produce reliable results over a long period of time. We couldn't do any of this without the grid.''

Anyone can join the GIMPS effort, downloading free software onto their machines that replaces their screen saver and uses the computer's idle time to study different numbers.

Prime numbers, which have long fascinated mathematicians, are integers greater than one that only can be divided by one and itself. The first prime numbers are 2,3, 5, 7 and 11. The number 2 is the only even prime number.

A Mersenne prime number is a prime that flows from the equation 2 to the P minus 1. The first Mersenne primes are 3, 7, 31 and 127.

Woltman explains that the Mersenne algorithm makes it easier to find these large prime numbers. He notes that when you get upwards of 20,000 or 30,000 digits it simply becomes too taxing to find a prime number without an algorithm. It would take too much time and too much computing power to make it feasible.

Each computer on the GIMPS grid runs software that can be downloaded for free from the GIMPS Web site. Every computer tests one or two numbers per month, depending on the amount of power in each system. The individual computers communicate with a main server, maintained by Scott Kurowski at Entropia, Inc., a Carlsbad, Calif.-based grid computing company.

Woltman reports that the GIMPS grid, which runs at 18 trillion calculations per second, covers every time zone in the world.

The Electronic Frontier Foundation is offering a $100,000 reward for the discovery of the first 10-million-digit prime number. And Woltman says the GIMPS project is working toward that goal.

''We'll find it in 2006 or 2007,'' he says. ''Probably 2007 would be my guess. Or we could run into a dry spell and it could take a lot longer. You never know when it's going to pop up.''

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