Two largest known prime numbers discovered just two weeks apart, one qualifies for $100k prize

Two new records for the largest known prime number have been set, both breaking the 10 million digit threshold. On August 23, Edson Smith, a systems engineer for the Program in Computing laboratory at the University of California, Los Angeles in California, United States, confirmed the primality of the number through his work as a volunteer in the distributed computing project known as the Great Internet Mersenne Prime Search, or GIMPS. This new prime qualifies GIMPS for a $100,000 award from the Electronic Frontier Foundation (EFF), offered to the first person or group to discover a prime number of 10 million digits or more. According to GIMPS' prize agreement, $50,000 will be given to the UCLA Department of Mathematics, $25,000 will be given to charity, $20,000 will be split among previous discoverers of Mersenne primes, and GIMPS will keep the remainder for funding and other uses. Smith, who was contacted by Scientific American by phone, said that the discovery was "quite unexpected."

Just two weeks later, on September 6, another Mersenne prime was discovered, this time by German electrical engineer Hans-Michael Elvenich, who worked for the chemical company Lanxess in Germany. This number is expressed as two to the 37,156,667th power minus one, and is 11,185,272 digits long. However, since this prime number was discovered later than the one found on August 23, it does not qualify for the EFF prize. Elvenich said that it was a "finally a great success" after having participated in GIMPS for four years.

A prime number is a positive integer that can be evenly divided only by 1 and itself. For example, 2, 3 and 11 are prime numbers. 21 is not a prime number because it is a product of 3 and 7. This new prime number is expressed as two to the 43,112,609th power minus one, and consists of 12,978,189 base 10 digits when written out. This type of prime number is called a Mersenne prime, one which can be expressed as one less than a power of two. Mersenne primes are rare, and only 46 are known up to now. The first few Mersenne primes are 3, 7, 31, 127 and 8191.

Both of these numbers took over a week to verify, using different software and hardware. The two primes were announced by GIMPS on September 16. Before these two discoveries, the two previously largest known prime numbers were discovered by UCMO professors Curtis Cooper and Steven Boone in Missouri, United States, and their record lasted almost three years. Historically, prime numbers discovered by GIMPS are larger than the one previously found. The only other exception was when the 29th Mersenne prime was discovered after the 30th and 31st were found.

Founded by M.I.T. graduate George Woltman in 1996, GIMPS has found 12 Mersenne primes, or about one per year on average. Volunteers who wish to help find primes can download a program called Prime95, which runs in the background.

Smaller prime numbers, such as those with a few hundred digits, are often used in cryptography. The recently discovered prime numbers are too large to have much practical use, but mathematics enthusiasts often seek them for fun. It is believed by some that such prime numbers may still have undiscovered uses.

Sources

Press Release: "GIMPS press release". Great Internet Mersenne Prime Search, September 16, 2008
John Matson "Big and bigger: New prime numbers claim top two spots". Scientific American, September 16, 2008
Eric W. Weisstein "45th and 46th Mersenne Primes Found". Wolfram Research, September 16, 2008
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Two largest known prime numbers discovered just two weeks apart, one qualifies for $100k prize

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