Grid Discovers Largest Known Prime Number

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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