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Revision as of 21:25, 29 May 2012 edit70.92.236.111 (talk)No edit summary← Previous edit Revision as of 09:22, 9 June 2012 edit undoToshio Yamaguchi (talk | contribs)Autopatrolled, Extended confirmed users17,397 edits expand table of largest currently known primesNext edit →
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| 9,808,358 | 9,808,358
| <ref name="MersenneDigitsAndNames"/> | <ref name="MersenneDigitsAndNames"/>
|-
| 5th
| 2<sup>30402457</sup>&nbsp;−&nbsp;1
| GIMPS
| 2005
| 9,152,052
| <ref name="TLKP">Samuel Yates, Chris Caldwell, . Retrieved on 2012-06-09.</ref>
|-
| 6th
| 2<sup>25964951</sup>&nbsp;−&nbsp;1
| GIMPS
| 2005
| 7,816,230
| <ref name="TLKP"/>
|-
| 7th
| 2<sup>24036583</sup>&nbsp;−&nbsp;1
| GIMPS
| 2004
| 7,235,733
| <ref name="TLKP"/>
|-
| 8th
| 2<sup>20996011</sup>&nbsp;−&nbsp;1
| GIMPS
| 2003
| 6,320,430
| <ref name="TLKP"/>
|-
| 9th
| 2<sup>13466917</sup>&nbsp;−&nbsp;1
| GIMPS
| 2001
| 4,053,946
| <ref name="TLKP"/>
|-
| 10th
| 19249×2<sup>13018586</sup>&nbsp;−&nbsp;1
| ]
| 2007
| 3,918,990
| <ref name="TLKP"/>
|-
|} |}


Revision as of 09:22, 9 June 2012

The largest known prime number is 2 - 1, the largest integer that is currently known to be a prime number.

Graph of number of digits in largest known prime by year, since the electronic computer. Note that the vertical scale is logarithmic.

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 Reference
1st 2 − 1 GIMPS 23 August 2008 12,978,189
2nd 2 − 1 GIMPS April 2009 12,837,064
3rd 2 − 1 GIMPS 6 September 2008 11,185,272
4th 2 − 1 GIMPS 4 September 2006 9,808,358
5th 2 − 1 GIMPS 2005 9,152,052
6th 2 − 1 GIMPS 2005 7,816,230
7th 2 − 1 GIMPS 2004 7,235,733
8th 2 − 1 GIMPS 2003 6,320,430
9th 2 − 1 GIMPS 2001 4,053,946
10th 19249×2 − 1 Seventeen or Bust 2007 3,918,990

GIMPS found the 11 latest records on ordinary computers operated by participants around the world.

The current record

The record is currently held by 2 − 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. Time called it the 29th top invention of 2008.

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.

Number Digits Year found
M127 39 1876
180×(M127) + 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
391581×2 − 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

References

  1. ^ "Record 12-Million-Digit Prime Number Nets $100,000 Prize". Electronic Frontier Foundation. Electronic Frontier Foundation. October 14, 2009. Retrieved November 26, 2011.
  2. ^ Chris Caldwell, The largest known primes. Retrieved on 2009-06-14.
  3. ^ Chris Caldwell, The largest known prime by year.
  4. Electronic Frontier Foundation, Big Prime Nets Big Prize.
  5. ^ Landon Curt Noll, Mersenne Prime Digits and Names. Retrieved on 2011-01-03.
  6. ^ Samuel Yates, Chris Caldwell, The largest known primes. Retrieved on 2012-06-09.
  7. "Best Inventions of 2008 - 29. The 46th Mersenne Prime". Time. Time Inc. Retrieved January 17, 2012.

External links

Prime number classes
By formula
By integer sequence
By property
Base-dependent
Patterns
k-tuples
By size
  • Mega (1,000,000+ digits)
  • Largest known
    • Complex numbers
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    Related topics
    First 60 primes
    List of prime numbers
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