The largest known prime number is 243112609 − 1, 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.
The fast Fourier transform implementation of the Lucas–Lehmer primality test for Mersenne numbers is fast compared to other known primality tests for other kinds of numbers. Due in part to this and to the historical interest in Mersenne primes, many of the largest known primes are Mersenne primes. As of April 2011 the nine largest known primes are Mersenne primes, while the tenth is the largest known non-Mersenne prime. 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.
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. In 2008 the record passed ten million digits, earning a $100,000 prize. Additional prizes are being offered for the first prime number found with at least one hundred million digits and the first with at least one billion digits.
| Rank | Prime number | Found by | Found date | Number of digits | |
|---|---|---|---|---|---|
| 1st | 243,112,609 − 1 | GIMPS | 2008 August 23 | 12,978,189 | |
| 2nd | 242,643,801 − 1 | GIMPS | 2009 April 12 | 12,837,064 | |
| 3rd | 237,156,667 − 1 | GIMPS | 2008 September 6 | 11,185,272 | |
| 4th | 232,582,657 − 1 | GIMPS | 2006 September 4 | 9,808,358 | |
| 5th | 230,402,457 − 1 | GIMPS | 2005 December 15 | 9,152,052 | |
| 6th | 225,964,951 − 1 | GIMPS | 2005 February 18 | 7,816,230 | |
| 7th | 224,036,583 − 1 | GIMPS | 2004 May 15 | 7,235,733 | |
| 8th | 220,996,011 − 1 | GIMPS | 2003 November 17 | 6,320,430 | |
| 9th | 213,466,917 − 1 | GIMPS | 2001 November 14 | 4,053,946 | |
| 10th | 19,249×213,018,586 + 1 | Seventeen or Bust | 2007 March 26 | 3,918,990 |
GIMPS found the 11 latest records on ordinary computers operated by participants around the world.
Read more about Largest Known Prime Number: The Current Record, History
Famous quotes containing the words largest, prime and/or number:
“The eager fate which carried thee
Took the largest part of me:
For this losing is true dying;
This is lordly man’s down-lying,
This his slow but sure reclining,
Star by star his world resigning.”
—Ralph Waldo Emerson (1803–1882)
“I came there as prime steak and now I feel like low-grade hamburger.”
—Joycelyn Elders (b. 1933)
“My idea is that the world outside—the so-called modern world—can only pervert and degrade the conceptions of the primitive instinct of art and feeling, and that our only chance is to accept the limited number of survivors—the one- in-a-thousand of born artists and poets—and to intensify the energy of feeling within that radiant centre.”
—Henry Brooks Adams (1838–1918)