Largest known prime number
- Largest known prime number
The largest known prime number is the largest integer that is currently known to be a prime number.
It was proven by Euclid that there are infinitely many prime numbers; thus, there is always a prime greater than the largest known prime. Many mathematicians and hobbyists search for large prime numbers. There are several prizes offered by the Electronic Frontier Foundation for record primes. [ [http://www.eff.org/awards/coop.php Electronic Frontier Foundation: Cooperative Computing Awards] ]
Because the FFT implementation of the Lucas–Lehmer test for Mersenne numbers is faster than other known primality tests for other kinds of primes, many of the largest known primes are Mersenne primes. As of September 2008 there were eight Mersenne primes among the ten largest known primes. [Chris Caldwell, [http://primes.utm.edu/largest.html The largest known primes] ] The last 14 record primes were Mersenne primes. Before that was a single non-Mersenne (improving the record by merely 37 digits in 1989), and 17 more Mersenne primes going back to 1952. [Chris Caldwell, [http://primes.utm.edu/notes/by_year.html The largest known prime by year] ]
The use of electronic computers has accelerated the discoveries and found all records since 1951. The record passed one million digits in 1999, earning a $50,000 prize. [Electronic Frontier Foundation, [http://www.eff.org/awards/20000406_coopaward_pr.html Big Prime Nets Big Prize] ]
As of September 2008, the largest known prime was discovered by the distributed computing project Great Internet Mersenne Prime Search (GIMPS):
:243,112,609 − 1.
This was found to be a prime number on August 23 2008. This number is 12,978,189 digits long and is (chronologically) the 45th known Mersenne prime.
Its predecessor as largest known prime, 232,582,657 − 1, was first shown to be prime on September 4 2006 by GIMPS also. GIMPS found the 11 latest records on ordinary computers operated by participants around the world.
References
External links
* [http://www.mersenne.org/m45and46.htm Press release about the largest known prime 243,112,609−1]
* [http://prime.isthe.com/no.index/chongo/merdigit/long-m43112609/prime-c.html Decimal expansion of 243,112,609−1]
* [http://mersenne.org/32582657.htm Press release about the former largest known prime 232,582,657−1]
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