Largest known prime

From Wikipedia, the free encyclopedia

Graph of number of digits in largest known prime by year - electronic era. Note that the vertical scale is logarithmic.

It was proven by Euclid that there are infinitely many prime numbers; thus, there is no "largest prime number". However, many math professionals and hobbyists enjoy searching for large prime numbers. This may also be profitable as there are several prizes offered by the Electronic Frontier Foundation for record primes.^[1]

Many of the largest known primes are Mersenne primes. As of January 2007 there were seven Mersenne primes among the ten largest known primes.^[2] The last 13 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.^[3]

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.^[4]

As of January 2007, the largest known prime was discovered by the distributed computing project Great Internet Mersenne Prime Search (GIMPS):

2^32,582,657 − 1.

This was confirmed to be a prime number on September 11, 2006. This number is 9,808,358 digits long and is the 44th known Mersenne prime.

Its predecessor as largest known prime, 2^30,402,457 − 1, was first shown to be prime on December 15, 2005 by GIMPS also. GIMPS found the 10 latest records on ordinary computers operated by participants around the world.

There is a $100,000 prize for the first known prime with at least 10,000,000 digits. It seems likely that this prize will be given to the next record prime as the current record is close to this mark. A Mersenne prime 2^p − 1 with p ≥ 33,219,281 would have at least 10,000,000 digits, and GIMPS is testing many candidates of this size.