A participant in the Great Internet Mersenne Prime Search (GIMPS) has identified the largest prime number yet. When printed out, its digits would fill more than 450 pages of Science News.
Discovered by 20-year-old Michael Cameron of Owen Sound, Ontario, the new champion prime is 213,466,917 – 1, which runs to 4,053,946 decimal digits.
A prime is a whole number evenly divisible by only itself and 1. Cameron’s number belongs to a special class of extremely rare primes named after 17th-century mathematician Marin Mersenne.
A Mersenne number can be expressed in the form 2p – 1, where the exponent p is a prime. Only a handful of these numbers are also themselves prime. The new record holder is just the 39th known Mersenne prime.
Cameron discovered the record-setting prime using software written by George Woltman, a retired computer programmer in Orlando, Fla. Woltman started the GIMPS project in 1996. By downloading software available at www.mersenne.org to their home or office computers, GIMPS volunteers can test Mersenne numbers for primality whenever their machines are otherwise idle.
Cameron’s desktop computer ran part-time for 45 days to prove that the Mersenne number, 213,466,917 – 1, is prime. Independent verification of the discovery, completed last week, required 3 weeks on a powerful workstation.
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The GIMPS effort relies on networking software developed by Scott Kurowski of Entropia, a computing-technology company in San Diego. His PrimeNet computer system distributes work to, and gathers results from, more than 200,000 computers scattered throughout the world. The GIMPS project has helped catalyze the development of such systems for handling massive amounts of data processing over the Internet (SN: 3/4/00, p. 152: https://www.sciencenews.org/20000304/bob1.asp).
Mersenne primes themselves are of interest to computational number theorists, who pursue such basic questions as the distribution of primes among all whole numbers. Volunteers haven’t yet tested every Mersenne number smaller than the current champion, so another Mersenne prime may yet lurk among the untested numbers.
“There are more primes out there,” Woltman says, “and anyone with a reasonably powerful personal computer can join GIMPS and become a big prime hunter.”