Carleton student helps pin down largest known prime number

A Carleton University doctoral student has helped an international team of mathematicians discover the largest known prime number, a number so long it would fill 3,200 pages if written down.

A doctoral student at Carleton University in Ottawa has helped an international team of mathematicians discover the largest known prime number — a number so long it would fill over 3,200 pages if written down.

A prime number can be equally divided only by the number one and itself. Simple examples include two, three, five, seven and 11.

Using network of supercomputers, Jeff Gilchrist was one of several volunteers who helped verify the number, which contains a whopping 12.9 million digits.

"If you printed that number out, it would be over 3,000 pages long. So it would be several volumes and a series of books, for sure," Gilchrist told CBC News.

Edson Smith, a computing manager in the math department at the University of California at Los Angeles, led the team that made the initial discovery. To ensure reliability of the results, Gilchrist and other verifiers had to use a different computer program and different hardware.

Wins $100,000 award

It is the first prime number ever discovered with more than 10 million digits, a benchmark which qualifies the achievement for a $100,000 U.S. Co-operative Computing Award offered by the Electronic Frontier Foundation.

"It's pretty exciting," Gilchrist said. "It's quite an achievement."

The newly discovered number can be written in shorthand as two to the power of 43,112,609, minus one.

It's the sixth record-breaking number Gilchrist has co-verified. The first, in 2004, was seven million digits long. The previous record-holder, set in 2006, was about 9.8 million digits long.

The difficulty in discovering large prime numbers has led to their use in internet security and other cryptographic tools, but Gilchrist said their discovery also has value in assessing the speed and efficiency of computers.

"It helps let us know the state of the art of computing technology, how far we can push our computers and our software," he said.

To verify the most recent prime number, Gilchrist said it took 16 hours for the network of supercomputers provided by the Shared Hierarchical Academic Research Computing Network — a consortium of colleges and universities in Ontario.

To do the same task 10 years ago would have taken an entire year, he said.

"The number itself isn't that important. It's more what we are capable of finding now."