en>Julia Abril: clarify relation to Bessel

2014-11-26T08:24:23Z

clarify relation to Bessel

en>Brad7777: /* References */ changed catgeory mathematics to catgeory differential equations

2011-11-12T17:11:56Z

References: changed catgeory mathematics to catgeory differential equations

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A '''megaprime''' is a [[prime number]] with at least one million decimal digits<ref>Chris Caldwell, [http://primes.utm.edu/glossary/page.php?sort=Megaprime The Prime Glossary: megaprime] at The [[Prime Pages]]. Retrieved on 2008-01-04.</ref> (whereas [[titanic prime]] is a prime number with at least 1000 digits, and [[gigantic prime]] has at least 10000 digits).

[[File:Megaprime found.png|thumb|330px|The number of megaprimes found by year.]]

{{As of|2013|03|17}}, 63 megaprimes are known.<ref name="The_largest_known_primes">Chris Caldwell, [http://primes.utm.edu/primes/lists/short.txt The Largest Known Primes] at The Prime Pages. Retrieved on 2013-02-24.</ref> The first to be found was the [[Mersenne prime]] 26972593−1 with 2,098,960 digits, discovered in 1999 by Nayan Hajratwala, a participant in the [[distributed computing]] project [[GIMPS]].<ref>[[GIMPS]] press release, [http://www.mersenne.org/primes/6972593.htm ''GIMPS Finds First Million-Digit Prime'']. Retrieved on 2008-01-04.</ref><ref name="largest">Chris Caldwell, [http://primes.utm.edu/notes/by_year.html ''The Largest Known Prime by Year: A Brief History''] at The Prime Pages. Retrieved on 2008-09-28.</ref>

The term '''bevaprime''' has been proposed as a term for a prime with at least 1,000,000,000 digits.<ref name="largest"/>

==Known megaprimes and mega PRPs==

Entries labelled "Prime" have been proved prime; those labelled "PRP" have not. See the article [[Probable prime]].

{| class="wikitable" border="1"
|-
! Number
! Discovery date
! Decimal digits
! Prime / [[probable prime|PRP]]
|-
| 257885161 – 1
| 2013-01-25
| 17,425,170
| Prime
|-
| 243112609 – 1
| 2008-08-23
| 12,978,189
| Prime
|-
| 242643801 – 1
| 2009-04-12
| 12,837,064
| Prime
|-
| 237156667 – 1
| 2008-09-06
| 11,185,272
| Prime
|-
| 232582657 – 1
| 2006
| 9,808,358
| Prime
|-
| 230402457 – 1
| 2005-12-15
| 9,152,052
| Prime
|-
| 225964951 – 1
| 2005-02-18
| 7,816,230
| Prime
|-
| 224036583 – 1
| 2004-05-15
| 7,235,733
| Prime
|-
| 220996011 – 1
| 2003-11-17
| 6,320,430
| Prime
|-
| 213466917 – 1
| 2001-11-14
| 4,053,946
| Prime
|-
| 19249×213018586 + 1{{align|right|<ref name="The_largest_known_primes"/>}}
| 2007-03-26
| 3,918,990
| Prime
|-
| 475856524288 + 1{{align|right|<ref>[http://www.primegrid.com/download/GFN-475856_524288.pdf Official announcement of discovery of 475856524288 + 1], PrimeGrid</ref>}}
| 2012-08-08
| 2,976,633
| Prime
|-
| 356926524288 + 1{{align|right|<ref>[http://www.primegrid.com/download/GFN-356926_524288.pdf Official announcement of discovery of 356926524288 + 1], PrimeGrid</ref>}}
| 2012-06-20
| 2,911,151
| Prime
|-
| 341112524288 + 1{{align|right|<ref>[http://www.primegrid.com/download/GFN-341112_524288.pdf Official announcement of discovery of 341112524288 + 1], PrimeGrid</ref>}}
| 2012-06-15
| 2,900,832
| Prime
|-
| 27653×29167433 + 1{{align|right|<ref name="The_largest_known_primes"/>}}
| 2005
| 2,759,677
| Prime
|-
| 90527 × 29162167 + 1
| 2010
| 2,758,093
| Prime
|-
| 29092392 + 40291{{align|right|<ref name=PRPTop>[http://www.primenumbers.net/prptop/prptop.php Probable Primes Top 10000], primenumbers.net</ref>}}
| 2011-02
| 2,737,083
| PRP
|-
| 75898524288 + 1{{align|right|<ref>[http://www.primegrid.com/download/gfn-75898_524288.pdf Official announcement of discovery of 75898524288 + 1], PrimeGrid</ref>}}
| 2011-11-19
| 2,558,647
| Prime
|-
| 28433×27830457 + 1{{align|right|<ref name="The_largest_known_primes"/>}}
| 2004
| 2,357,207
| Prime
|-
| 3×27033641 + 1{{align|right|<ref>[http://www.primegrid.com/download/321-7033641.pdf Official announcement of discovery of 3×27033641 + 1], PrimeGrid</ref>}}
| 2011-02-21
| 2,117,338
| Prime
|-
| 33661×27031232 + 1{{align|right|<ref name="The_largest_known_primes"/>}}
| 2007
| 2,116,617
| Prime
|-
| 26972593 – 1
| 1999-06-01
| 2,098,960
| Prime
|-
| 6679881×26679881 + 1{{align|right|<ref>[http://www.primegrid.com/download/cullen-6679881.pdf Official announcement of discovery of 6679881×26679881 + 1], PrimeGrid</ref>}}
| 2009-07-25
| 2,010,852
| Prime
|-
| 6328548×26328548 + 1{{align|right|<ref>[http://www.primegrid.com/download/cullen-6328548.pdf Official announcement of discovery of 6328548×26328548 + 1], PrimeGrid</ref>}}
| 2009-04-20
| 1,905,090
| Prime
|-
| 3×26090515 – 1{{align|right|<ref>[http://www.primegrid.com/download/321-6090515.pdf Official announcement of discovery of 3×26090515 – 1], PrimeGrid</ref>}}
| 2010-04-24
| 1,833,429
| Prime
|-
| 7×25775996 + 1{{align|right|<ref>[http://www.primegrid.com/download/PPS-5775996.pdf Official announcement of discovery of 7×25775996 + 1], PrimeGrid</ref>}}
| 2012-11-02
| 1,738,749
| Prime
|-
| 252191×25497878 – 1{{align|right|<ref>[http://www.primegrid.com/download/TRP-252191.pdf Official announcement of discovery of 252191×25497878 – 1], PrimeGrid</ref>}}
| 2012-06-23
| 1,655,032
| Prime
|-
| 258317 × 25450519+1
| 2008
| 1,640,776
| Prime
|-
| 25146295 + 41693{{align|right|<ref name=PRPTop/>}}
| 2009-11
| 1,549,190
| PRP
|-
| 773620262144 + 1{{align|right|<ref>[http://www.primegrid.com/download/gfn-773620_262144.pdf Official announcement of discovery of 773620262144 + 1], PrimeGrid</ref>}}
| 2012-04-19
| 1,543,643
| Prime
|-
| 3×25082306 + 1{{align|right|<ref>[http://www.primegrid.com/download/321-5082306.pdf Official announcement of discovery of 3×25082306 + 1], PrimeGrid</ref>}}
| 2009-04-03
| 1,529,928
| Prime
|-
| 676754262144+1
| 2012
| 1,528,413
| Prime
|-
| 5359 × 25054502+1
| 2003
| 1,521,561
| Prime
|-
| 525094262144+1
| 2012
| 1,499,526
| Prime
|-
| 265711 × 24858008+1
| 2008
| 1,462,412
| Prime
|-
| 1271 × 24850526-1
| 2012
| 1,460,157
| Prime
|-
| 361658262144+1
| 2011
| 1,457,075
| Prime
|-
| 9 × 24683555-1
| 2012
| 1,409,892
| Prime
|-
| 24583176 + 2131{{align|right|<ref name=PRPTop/>}}
| 2009-09
| 1,379,674
| PRP
|-
| 121×24553899 – 1{{align|right|<ref>[http://www.primegrid.com/download/27121-4553899.pdf Official announcement of discovery of 121×24553899 – 1], PrimeGrid</ref>}}
| 2012-02-25
| 1,370,863
| Prime
|-
| 145310262144+1
| 2011
| 1,353,265
| Prime
|-
| 353159×24331116 – 1{{align|right|<ref>[http://www.primegrid.com/download/trp-353159.pdf Official announcement of discovery of 353159×24331116 – 1], PrimeGrid</ref>}}
| 2011-05-31
| 1,303,802
| Prime
|-
| 141941×24299438 – 1{{align|right|<ref>[http://www.primegrid.com/download/trp-141941.pdf Official announcement of discovery of 141941×24299438 – 1], PrimeGrid</ref>}}
| 2011-05-26
| 1,294,265
| Prime
|-
| 15 × 24246384+1
| 2013
| 1,278,291
| Prime
|-
| 3×24235414 – 1{{align|right|<ref>[http://www.primegrid.com/download/321-4235414.pdf Official announcement of discovery of 3×24235414 – 1], PrimeGrid</ref>}}
| 2008-03-23
| 1,274,988
| Prime
|-
| 191 × 24203426-1
| 2012
| 1,265,360
| Prime
|-
| <math>\tfrac{2^{4031399}+1}{3}</math>{{align|right|<ref name=PRPTop/>}}
| 2010-02
| 1,213,572
| PRP
|-
| 40734262144+1
| 2011
| 1,208,473
| Prime
|-
| 9 × 24005979-1
| 2012
| 1,205,921
| Prime
|-
| 27×23855094 – 1{{align|right|<ref>[http://www.primegrid.com/download/27121-3855094.pdf Official announcement of discovery of 27×23855094 – 1], PrimeGrid</ref>}}
| 2012-02-28
| 1,160,501
| Prime
|-
| 24518262144+1
| 2008
| 1,150,678
| Prime
|-
| 123547×23804809 – 1{{align|right|<ref>[http://www.primegrid.com/download/trp-123547.pdf Official announcement of discovery of 123547×23804809 – 1], PrimeGrid</ref>}}
| 2011-05-08
| 1,145,367
| Prime
|-
| 415267×23771929 – 1{{align|right|<ref>[http://www.primegrid.com/download/trp-415267.pdf Official announcement of discovery of 415267×23771929 – 1], PrimeGrid</ref>}}
| 2011-05-08
| 1,135,470
| Prime
|-
| 11 × 23771821+1
| 2013
| 1,135,433
| Prime
|-
| 938237 × 23752950-1
| 2007
| 1,129,757
| Prime
|-
| 65531 × 23629342-1
| 2011
| 1,092,546
| Prime
|-
| 485767 × 23609357-1
| 2008
| 1,086,531
| Prime
|-
| 5 × 23569154-1
| 2009
| 1,074,424
| Prime
|-
| 1019 × 23536312-1
| 2012
| 1,064,539
| Prime
|-
| 7 × 23511774+1
| 2008
| 1,057,151
| Prime
|-
| 428639 × 23506452-1
| 2011
| 1,055,553
| Prime
|-
| 9×23497442 + 1{{align|right|<ref>[http://www.primegrid.com/download/PPS-3497442.pdf Official announcement of discovery of 9×23497442 + 1], PrimeGrid</ref>}}
| 2012-10-23
| 1,052,836
| Prime
|-
| 1273 × 23448551-1
| 2012
| 1,038,121
| Prime
|-
| 191249 × 23417696-1
| 2010
| 1,028,835
| Prime
|-
| 59 × 23408416-1
| 2010
| 1,026,038
| Prime
|-
| 81×23352924 + 1{{align|right|<ref>[http://www.primegrid.com/download/mega-3352924.pdf Official announcement of discovery of 81×23352924 + 1], PrimeGrid</ref>}}
| 2012-01-17
| 1,009,333
| Prime
|-
| 1087 × 23336385-1
| 2012
| 1,004,355
| Prime
|-
| 464253×23321908 – 1{{align|right|<ref name="The_largest_known_primes"/>}}
| 2013
| 1,000,000
| Prime
|-
| 10999999 + 593499{{align|right|<ref>Patrick De Geest, [http://www.worldofnumbers.com/em_megaprp.htm 10^999999 + y], World!Of Numbers</ref>}}
| 2012-12-24
| 1,000,000
| PRP
|}

== See also ==
* [[Largest known prime number]]
* [[Electronic Frontier Foundation#Awards|Electronic Frontier Foundation—Awards]]

==References==
{{Reflist|colwidth=30em}}

==External links==
* Chris Caldwell, [http://primes.utm.edu/primes/ The Largest Known Primes Database] at The Prime Pages.
* [http://www.primegrid.com/download/321-6090515.pdf PrimeGrid’s 321 Prime Search], about the discovery of 3×26090515−1.

{{Prime number classes}}

[[Category:Prime numbers]]

{{Num-stub}}

[[fr:Nombre premier#Jalons symboliques]]

Cylindrical harmonics - Revision history

en>Julia Abril: clarify relation to Bessel

en>Brad7777: /* References */ changed catgeory mathematics to catgeory differential equations