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.[1]
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[update] the nine largest known primes are Mersenne primes, while the tenth is the largest known non-Mersenne prime.[2] 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.[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] In 2008 the record passed ten million digits, earning a $100,000 prize.[1] 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.[1]
| Rank | Prime number | Found by | Found date | Number of digits | Reference |
|---|---|---|---|---|---|
| 1st | 243,112,609 − 1 | GIMPS | 23 August 2008 | 12,978,189 | [2] |
| 2nd | 242,643,801 − 1 | GIMPS | April 2009 | 12,837,064 | [5] |
| 3rd | 237,156,667 − 1 | GIMPS | 6 September 2008 | 11,185,272 | [5] |
| 4th | 232,582,657 − 1 | GIMPS | 4 September 2006 | 9,808,358 | [5] |
GIMPS found the 11 latest records on ordinary computers operated by participants around the world.
Contents |
[edit] The current record
The record is currently held by 243,112,609 − 1 with 12,978,189 digits. Its discovery resulted from the Great Internet Mersenne Prime Search (GIMPS), and won its discoverers $100,000 and a Cooperative Computing Award from the Electronic Frontier Foundation for discovering a prime number of over 10 million digits.[1] Time called it the 29th top invention of 2008.[6]
[edit] History
The following table lists the progression of the largest known prime number in ascending order, where Mn is a Mersenne number with exponent n.[3]
| Number | Digits | Year found |
|---|---|---|
| M127 | 39 | 1876 |
| 180×(M127)2 + 1 | 79 | 1951 |
| M521 | 157 | 1952 |
| M607 | 183 | 1952 |
| M1279 | 386 | 1952 |
| M2203 | 664 | 1952 |
| M2281 | 687 | 1952 |
| M3217 | 969 | 1957 |
| M4423 | 1332 | 1961 |
| M9689 | 2917 | 1963 |
| M9941 | 2993 | 1963 |
| M11213 | 3376 | 1963 |
| M19937 | 6002 | 1971 |
| M21701 | 6533 | 1978 |
| M23209 | 6987 | 1979 |
| M44497 | 13395 | 1979 |
| M86243 | 25962 | 1982 |
| M132049 | 39751 | 1983 |
| M216091 | 65050 | 1985 |
| 391581×2216193 − 1 | 65087 | 1989 |
| M756839 | 227832 | 1992 |
| M859433 | 258716 | 1994 |
| M1257787 | 378632 | 1996 |
| M1398269 | 420921 | 1996 |
| M2976221 | 895932 | 1997 |
| M3021377 | 909526 | 1998 |
| M6972593 | 2098960 | 1999 |
| M13466917 | 4053946 | 2001 |
| M20996011 | 6320430 | 2003 |
| M24036583 | 7235733 | 2004 |
| M25964951 | 7816230 | 2005 |
| M30402457 | 9152052 | 2005 |
| M32582657 | 9808358 | 2006 |
| M43112609 | 12978189 | 2008 |
[edit] References
- ^ a b c d "Record 12-Million-Digit Prime Number Nets $100,000 Prize". Electronic Frontier Foundation. Electronic Frontier Foundation. October 14, 2009. https://www.eff.org/press/archives/2009/10/14-0. Retrieved November 26, 2011.
- ^ a b Chris Caldwell, The largest known primes. Retrieved on 2009-06-14.
- ^ a b Chris Caldwell, The largest known prime by year.
- ^ Electronic Frontier Foundation, Big Prime Nets Big Prize.
- ^ a b c Landon Curt Noll, Mersenne Prime Digits and Names. Retrieved on 2011-01-03.
- ^ "Best Inventions of 2008 - 29. The 46th Mersenne Prime". Time. Time Inc. http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html. Retrieved January 17, 2012.
