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:
“Because it is in the nature of things that they become extreme, we have passed down from manliness to cruelty. If I had been told when I was 20 that there was a tavern in the town where the brave and the cruel were gathered together, I would have run all the way and I would have gone up to the largest and leatheriest of the denizens and said: “If you truly love me, kill the bartender.””
—Quentin Crisp (b. 1908)
“By whatever means it is accomplished, the prime business of a play is to arouse the passions of its audience so that by the route of passion may be opened up new relationships between a man and men, and between men and Man. Drama is akin to the other inventions of man in that it ought to help us to know more, and not merely to spend our feelings.”
—Arthur Miller (b. 1915)
“... in every State there are more women who can read and write than the whole number of illiterate male voters; more white women who can read and write than all Negro voters; more American women who can read and write than all foreign voters.”
—National Woman Suffrage Association. As quoted in History of Woman Suffrage, vol. 4, ch. 13, by Susan B. Anthony and Ida Husted Harper (1902)