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Mathematician: Finding 17M-digit prime number like climbing Everest

Computer that discovered latest Mersenne prime did 57M calculations over 39 days

The mathematician who found the largest known prime number said the discovery last month was like climbing Mount Everest or landing on the moon.

The prime number, which is more than 17 million digits long, won't make computers run faster or help scientists develop better rockets. However, searching for the number was an exhilarating journey for Curtis Cooper, a mathematician at the University of Central Missouri.

If this prime number -- 257,885,161 minus 1 - was typed out in a standard Times Roman 12-point font, it would span more than 30 miles. It also would fill more than six Bibles.

It is the third prime number discovery he has made, and Cooper said the discovery isn't any less exciting. He said the feat, for a mathematician, was like climbing Mount Everest, because it was a goal he set out to achieve because he wanted to do, not that he needed to.

"We've been working on this for years," Cooper told Computerworld. "We probably finish 50, 60 or 70 numbers per day, and for years we didn't find anything. Then on Jan. 25 we hit the jackpot. It's truly like looking for a needle in a haystack." He said the feat, for a mathematician, was was like climbing Mount Everest, explaining it was a goal he had set out to achieve because it was something he wanted to do, not that he needed to.

The Great Internet Mersenne Prime Search (GIMPS), a 16-year-old project that uses a grid of computers provided by volunteers to find large prime numbers, announced Tuesday that Cooper discovered the 48th known Mersenne prime.

A prime number is a whole number that can be divided only by one and itself. A Mersenne prime number is a class of primes named after Marin Mersenne, a 17th century French monk who studied the rare numbers more than 350 years ago.

Mersenne primes are extremely rare. With this discovery, only 48 are known. Each Mersenne prime is increasingly difficult to find.

Mersenne Primes are 2 raised to the x power, minus 1. For instance, the number 3 is a Mersenne prime number because it can be written as 2 squared, minus one. Number 7 is also a Mersenne prime number because it's 2 cubed, minus one.

To find this new Mersenne prime, Cooper used 1,000 computers on his university campus in Warrensburg, Mo. Each computer checked individual numbers. Dual-core machines could check two numbers at once.

The computer that discovered this 17 million-digit prime is a Dell desktop running an Intel dual-core processor. Sitting in the university's modern language lab, the computer spent 39 days running 57 million calculations to test the number.

In 1997, when Cooper and the university first began searching for Mersenne primes, he only had four computers in the project.

"We didn't have a server so I had to watch each machine," he said. "I thought that four computers was about all I could handle. But as we got a server, and a lot of the work was automated and the software got better, we were able to add so many more computers. I really like the process of having a goal in mind and working for that goal. Every morning I wake up and check our machines and see how they're doing. I really just love the process."

To verify the new Mersenne prime number, it was independently tested using different programs running on different hardware, according to the GIMPS organization. One verification test, which lasted 3.6 days, used an Nvidia GPU, and another used an Intel Core i7 CPU and ran for 4.5 days.

Cooper discovered his first record-breaking prime number in 2005. He found the second in 2006.

Mathematicians at UCLA broke Cooper's record in 2008. That record Mersenne prime number held until Cooper and the University of Central Missouri reclaimed it with this latest discovery.

The GIMPS organization will award $3,000 to Cooper, who is donating the money to the university since it provided the computers for his project.

Sharon Gaudin covers the Internet and Web 2.0, emerging technologies, and desktop and laptop chips for Computerworld. Follow Sharon on Twitter at @sgaudin, on Google+ or subscribe to Sharon's RSS feed. Her email address is [email protected].

See more by Sharon Gaudin on Computerworld.com.

Read more about high performance computing in Computerworld's High Performance Computing Topic Center.


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