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# Largest prime number, for now, found

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The Sunway Bluelight supercomputer.Photo: Xinhua

A number,  N , that can be represented as 2{+n} - 1 is called a Mersenne number after Marin Mersenne, a French philosopher who first studied such numbers over three centuries ago. When both  N and n are prime numbers, however,  N  is called a Mersenne prime, a number very rare and difficult to find on the number line — even by supercomputers clocking hundreds of trillions of calculations per second.

Mersenne primes have limited practical applications, but the few themselves are very interesting. For instance, if you've played the game Tower of Hanoi, you'll know that solving, say, an 8-disc tower requires as many moves as the eighth Mersenne prime, 2,147,483,647; generally, an  x -disc tower requires as many moves as the x {+t}{+h}Mersenne prime.

On January 25, 2013, the largest prime number yet — the 48th Mersenne prime — was discovered: It's value is 2 {+5}{+7}{+,}{+8}{+8}{+5}{+,}{+1}{+6}{+1}  – 1, or 581,887,266...724,285,951. The number contains 17,425,170 digits.

The discovery, like that of all the major primes since 1997, was made at the Great Internet Mersenne Prime Search (GIMPS), a distributed computing network over the internet. Specifically, it was made on the computer of Curtis Cooper, a volunteer and mathematician. The network itself involves 360,000 CPUs peaking at 150 trillion calculations per second. In comparison, the Sunway Bluelight supercomputer at the National Supercomputing Centre, China — one of the world's fastest — clocks 1,070.6 trillion calculations per second at its peak.

Interestingly, this is the third Mersenne prime involving Cooper's system, although the first two, M43 and M44, were discovered on Cooper's and Steven Boone's 700- and 850-PC cluster, respectively.

The validity of M48 as a Mersenne prime was established by testing on four different machines, one of them running the MLucas software, two the CUDALucas software (with one of them on an NVidia GPU), and one using the GIMPS itself on an Intel i7 CPU.

For his discovery, Cooper will receive a cash-award of \$3,000 from the GIMPS' board of directors. The GIMPS itself, on the other hand, will now go after the \$150,000 up for grabs from the Electronic Frontier Foundation (EFF) for finding a prime (not necessarily a Mersenne prime) with 100 million digits.

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