Prime numbers have long held a special appeal among the mathematically minded, from the Greek astronomer Eratosthenes, who devised a method for finding primes some 2,200 years ago, to the cryptographers who made them the foundation of today’s encryption protocols. Primes, each of which is divisible only by 1 and itself, have even been subject to claims of numerical ownership: California computer consultant Roger Schlafly patented two of them in 1994.
Now, the distributed-computing consortium that discovered the six largest known primes is set to unveil two more—including, possibly, a $100,000 prize–winning whopper. (We reported on the preliminary findings last month.) The Great Internet Mersenne Prime Search (GIMPS), started in 1996, looks for prime numbers of the form 2n – 1, known as Mersenne primes, of which 44 have been identified so far (the new additions would be numbers 45 and 46).
The search, powered by hundreds of member computers around the world, is slow going: GIMPS estimates that testing a single number for primality on a 2-GHz Pentium 4 can take two months. So after two years of silence, the emergence of a pair of new Mersenne primes nearly simultaneously—one on August 23, one on September 6—is an unexpected burst of productivity. (A call to GIMPS founder George Woltman was not immediately returned.)
There’s a good chance that one of the new arrivals will qualify for a $100,000 prize from the Electronic Frontier Foundation (EFF), to be awarded to the first discoverer of a prime number with at least 10 million digits. (The current record holder, 232582657 – 1, discovered in 2006, fell just short at 9,808,358 digits.)
In any case, the two new additions are sure to rank in the top seven of all known primes once revealed—it’s already been shown that there are no unknown Mersenne primes smaller than the current holder of sixth place. And whatever the result, GIMPS is sure to soldier on: the EFF offers an even bigger prize—$150,000—for a prime of 100 million digits or more.
Further Reading: A Prime Patent ($)
Image: Marin Mersenne