Edit count of the user (user_editcount ) | null |
Name of the user account (user_name ) | '86.137.73.72' |
Age of the user account (user_age ) | 0 |
Groups (including implicit) the user is in (user_groups ) | [
0 => '*'
] |
Rights that the user has (user_rights ) | [
0 => 'createaccount',
1 => 'read',
2 => 'edit',
3 => 'createtalk',
4 => 'writeapi',
5 => 'viewmyprivateinfo',
6 => 'editmyprivateinfo',
7 => 'editmyoptions',
8 => 'abusefilter-log-detail',
9 => 'urlshortener-create-url',
10 => 'centralauth-merge',
11 => 'abusefilter-view',
12 => 'abusefilter-log',
13 => 'vipsscaler-test'
] |
Whether or not a user is editing through the mobile interface (user_mobile ) | true |
Whether the user is editing from mobile app (user_app ) | false |
Page ID (page_id ) | 1669332 |
Page namespace (page_namespace ) | 0 |
Page title without namespace (page_title ) | 'Largest known prime number' |
Full page title (page_prefixedtitle ) | 'Largest known prime number' |
Edit protection level of the page (page_restrictions_edit ) | [] |
Last ten users to contribute to the page (page_recent_contributors ) | [
0 => 'HersheysCB',
1 => 'Leafy46',
2 => '68.4.177.38',
3 => '67.70.0.68',
4 => 'MaxnaCarta',
5 => 'D.Lazard',
6 => '76.100.240.121',
7 => 'Danbloch',
8 => 'Kelvin XII',
9 => 'PrimeHunter'
] |
Page age in seconds (page_age ) | 601510021 |
Action (action ) | 'edit' |
Edit summary/reason (summary ) | '' |
Time since last page edit in seconds (page_last_edit_age ) | 2092752 |
Old content model (old_content_model ) | 'wikitext' |
New content model (new_content_model ) | 'wikitext' |
Old page wikitext, before the edit (old_wikitext ) | '{{short description|none}}
The '''largest known prime number''' is {{nowrap|2<sup>82,589,933</sup> − 1}}, a number which has 24,862,048 digits when written in [[base 10]]. It was found via a computer volunteered by Patrick Laroche of the [[Great Internet Mersenne Prime Search]] (GIMPS) in 2018.<ref name="GIMPS-2018">{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}</ref>
[[File:Digits in largest prime found as a function of time.svg|thumb|400px|A 2020 plot of the number of digits in the largest known prime by year, since the electronic computer. The vertical scale is [[logarithmic scale|logarithmic]].]]
A [[prime number]] is a [[natural number]] greater than 1 with no [[divisor]]s other than 1 and itself. According to [[Euclid's theorem]] there are infinitely many prime numbers, so there is no largest prime.
Many of the largest known primes are [[Mersenne prime]]s, numbers that are one less than a power of two, because they can utilize a [[Lucas–Lehmer primality test| specialized primality test]] that is faster than the general one. {{As of|2023|June}}, the six largest known primes are Mersenne primes.<ref>{{cite web |url=https://t5k.org/primes/search.php?Number=100 |title=The largest known primes – Database Search Output |publisher=Prime Pages |access-date=19 March 2023}}</ref> The last seventeen record primes were Mersenne primes.<ref name="computer history">{{cite web |url=http://t5k.org/notes/by_year.html |title=The Largest Known Prime by Year: A Brief History |first1=Chris |last1=Caldwell |publisher=Prime Pages |access-date=19 March 2023}}</ref><ref>The last non-Mersenne to be the largest known prime, was [http://t5k.org/primes/page.php?id=390 391,581 ⋅ 2<sup>216,193</sup> − 1]; see also [http://t5k.org/notes/by_year.html The Largest Known Prime by year: A Brief History] originally by Caldwell.</ref> The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2''<sup>k</sup>'' − 1 is simply ''k'' ones.<ref>{{Cite web|url=http://www.personal.psu.edu/sxt104/class/Math140H/PerfectNum.html|title=Perfect Numbers|website=Penn State University|access-date=6 October 2019|quote=An interesting side note is about the binary representations of those numbers...}}</ref>
==Current record==
The record is currently held by {{nowrap|2<sup>82,589,933</sup> − 1}} with 24,862,048 digits, found by [[Great Internet Mersenne Prime Search|GIMPS]] in December 2018.<ref name="GIMPS-2018">{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}</ref> The first and last 120 digits of its value are shown below:
{{quote|148894445742041325547806458472397916603026273992795324185271289425213239361064475310309971132180337174752834401423587560 ...
(24,861,808 digits skipped)
... 062107557947958297531595208807192693676521782184472526640076912114355308311969487633766457823695074037951210325217902591<ref>{{Cite web|url=https://www.mersenne.org/primes/press/M82589933.html|title = 51st Known Mersenne Prime Discovered}}</ref>
|sign=|source=|style=word-wrap: break-word}}
{{as of|2024|2}}, this prime has held the record for more than 5 years, longer than any other prime since M<sub>19937</sub> (which held the record for 7 years from 1971 to 1978).
==Prizes==
There are several prizes offered by the [[Electronic Frontier Foundation]] (EFF) for record primes.<ref name="prizes" /> A prime with one million digits was found in 1999, earning the discoverer a US$50,000 prize.<ref>Electronic Frontier Foundation, [https://www.eff.org/press/releases/big-prime-nets-big-prize Big Prime Nets Big Prize].</ref> In 2008, a ten-million digit prime won a US$100,000 prize and a [[Cooperative Computing Award]] from the EFF.<ref name="prizes">{{cite web |url=https://www.eff.org/press/archives/2009/10/14-0 |title=Record 12-Million-Digit Prime Number Nets $100,000 Prize |date=October 14, 2009 |work=Electronic Frontier Foundation |publisher=[[Electronic Frontier Foundation]] |access-date=November 26, 2011 }}</ref> ''[[Time (magazine)|Time]]'' called this prime the 29th top invention of 2008.<ref name="invention">{{cite news |url=http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html |archive-url=https://web.archive.org/web/20081102044641/http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html |url-status=dead |archive-date=November 2, 2008 |title=Best Inventions of 2008 - 29. The 46th Mersenne Prime |magazine=Time |publisher=[[Time Inc]] |access-date=January 17, 2012 |date=October 29, 2008}}</ref>
Both of these primes were discovered through the [[Great Internet Mersenne Prime Search]] (GIMPS), which coordinates long-range search efforts among tens of thousands of computers and thousands of volunteers. The $50,000 prize went to the discoverer and the $100,000 prize went to GIMPS. GIMPS will split the US$150,000 prize for the first prime of over 100 million digits with the winning participant. A further prize is offered for the first prime with at least one billion digits.<ref name="prizes" />
GIMPS also offers a US$3,000 research discovery award for participants who discover a new Mersenne prime of less than 100 million digits.<ref>{{cite web |title=GIMPS by Mersenne Research, Inc. |url=https://www.mersenne.org/legal/ |access-date=21 November 2022 |website=mersenne.org}}</ref>
==History of largest known prime numbers==
[[File:MersennePrimeStamp.gif|thumb|right|287px|Commemorative postmark used by the [[University of Illinois at Urbana–Champaign|UIUC]] Math Department after proving that M<sub>11213</sub> is prime]]
The following table lists the progression of the largest known prime number in ascending order.<ref name="computer history" /> Here {{nowrap|M<sub>''p''</sub> {{=}} 2<sup>''p''</sup> − 1}} is the Mersenne number with exponent ''p'', where ''p'' is a prime number. The longest record-holder known was {{nowrap|M<sub>19</sub> {{=}} 524,287}}, which was the largest known prime for 144 years. No records are known prior to 1456.
{{clear}}
{| class="wikitable sortable" border="1"
|-
! Number
! Decimal expansion<br/>(partial for numbers > M<sub>1000</sub>)
! Digits
! Year found
! Discoverer<br/>
|-
| M<sub>13</sub>
|style="text-align:right;"| 8,191
|style="text-align:right;"| 4
| 1456
| Anonymous
|-
| M<sub>17</sub>
|style="text-align:right;"| 131,071
|style="text-align:right;"| 6
| 1588
| [[Pietro Cataldi]]
|-
| M<sub>19</sub>
|style="text-align:right;"| 524,287
|style="text-align:right;"| 6
| 1588
| Pietro Cataldi
|-
| <math>\tfrac{2^{32}+1}{641}</math>
|style="text-align:right;"| 6,700,417
|style="text-align:right;"| 7
| 1732
| [[Leonhard Euler]]?<br>Euler did not explicitly publish the primality of 6,700,417, but the techniques he had used to factorise 2<sup>32</sup> + 1 meant that he had already done most of the work needed to prove this, and some experts believe he knew of it.<ref>{{Cite book|url=https://books.google.com/books?id=3c6iBQAAQBAJ&pg=PA43|title = How Euler Did Even More|isbn = 9780883855843|last1 = Edward Sandifer|first1 = C.|date = 19 November 2014| publisher=The Mathematical Association of America }}</ref>
|-
| M<sub>31</sub>
|style="text-align:right;"| [[2,147,483,647]]
|style="text-align:right;"| 10
| 1772
| Leonhard Euler
|-
| <math>\tfrac{10^{18}+1}{1000001}</math>
|style="text-align:right;"| 999,999,000,001
|style="text-align:right;"| 12
| 1851
| Included (but question-marked) in a list of primes by Looff. Given his uncertainty, some do not include this as a record.
|-
| <math>\tfrac{2^{64}+1}{274177}</math>
|style="text-align:right;"| 67,280,421,310,721
|style="text-align:right;"| 14
| 1855
| [[Thomas Clausen (mathematician)|Thomas Clausen]] (but no proof was provided).
<!--|-
| [M<sub>59</sub>/179951]
|style="text-align:right;"| [3,203,431,780,337]
|style="text-align:right;"| [13]
| [1867]
| Landry. A record if the immediately preceding entry is excluded.-->
|-
| M<sub>127</sub>
|style="text-align:right;"| 170,141,183,460,469,<wbr/>231,731,687,303,715,<wbr/>884,105,727
|style="text-align:right;"| 39
| 1876
| [[Édouard Lucas]]
|-
| <math>\tfrac{2^{148}+1}{17}</math>
|style="text-align:right;"| 20,988,936,657,440,<wbr/>586,486,151,264,256,<wbr/>610,222,593,863,921
|style="text-align:right;"| 44
| 1951
| [[Aimé Ferrier]] with a mechanical calculator; the largest record not set by computer.
|-
| 180×(M<sub>127</sub>)<sup>2</sup>+1
|
521064401567922879406069432539<wbr />095585333589848390805645835218<wbr />3851018372555735221
|style="text-align:right;"| 79
| 1951
| [[J. C. P. Miller]] & [[David Wheeler (computer scientist)|D. J. Wheeler]]<ref>[[J. C. P. Miller|J. Miller]], [https://doi.org/10.1038/168838b0 Large Prime Numbers]. ''Nature'' 168, 838 (1951).</ref><br />Using [[University of Cambridge Mathematical Laboratory|Cambridge's]] [[Electronic delay storage automatic calculator|EDSAC]] computer
|-
| M<sub>521</sub>
|
686479766013060971498190079908<wbr />139321726943530014330540939446<wbr />345918554318339765605212255964<wbr />066145455497729631139148085803<wbr />712198799971664381257402829111<wbr />5057151
|style="text-align:right;"| 157
| 1952
| [[Raphael M. Robinson]]
|-
| M<sub>607</sub>
|
531137992816767098689588206552<wbr />468627329593117727031923199444<wbr />138200403559860852242739162502<wbr />265229285668889329486246501015<wbr />346579337652707239409519978766<wbr />587351943831270835393219031728127
|style="text-align:right;"| 183
| 1952
| Raphael M. Robinson
|-
| M<sub>1279</sub>
| 104079321946...703168729087
|style="text-align:right;"| 386
| 1952
| Raphael M. Robinson
|-
| M<sub>2203</sub>
| 147597991521...686697771007
|style="text-align:right;"| 664
| 1952
| Raphael M. Robinson
|-
| M<sub>2281</sub>
| 446087557183...418132836351
|style="text-align:right;"| 687
| 1952
| Raphael M. Robinson
|-
| M<sub>3217</sub>
| 259117086013...362909315071
|style="text-align:right;"| 969
| 1957
| [[Hans Riesel]]
|-
| M<sub>4423</sub>
| 285542542228...902608580607
|style="text-align:right;"| 1,332
| 1961
| [[Alexander Hurwitz]]
|-
| M<sub>9689</sub>
| 478220278805...826225754111
|style="text-align:right;"| 2,917
| 1963
| [[Donald B. Gillies]]
|-
| M<sub>9941</sub>
| 346088282490...883789463551
|style="text-align:right;"| 2,993
| 1963
| Donald B. Gillies
|-
| M<sub>11213</sub>
| 281411201369...087696392191
|style="text-align:right;"| 3,376
| 1963
| Donald B. Gillies
|-
| M<sub>19937</sub>
| 431542479738...030968041471
|style="text-align:right;"| 6,002
| 1971
| [[Bryant Tuckerman]]
|-
| M<sub>21701</sub>
| 448679166119...353511882751
|style="text-align:right;"| 6,533
| 1978
| Laura A. Nickel and [[Landon Curt Noll]]<ref name="isthe">[[Landon Curt Noll]], [http://www.isthe.com/chongo/tech/math/prime/prime_press.html Large Prime Number Found by SGI/Cray Supercomputer].</ref>
|-
| M<sub>23209</sub>
| 402874115778...523779264511
|style="text-align:right;"| 6,987
| 1979
| Landon Curt Noll<ref name="isthe"/>
|-
| M<sub>44497</sub>
| 854509824303...961011228671
|style="text-align:right;"| 13,395
| 1979
| [[David Slowinski]] and [[Harry L. Nelson]]<ref name="isthe"/>
|-
| M<sub>86243</sub>
| 536927995502...709433438207
|style="text-align:right;"| 25,962
| 1982
| David Slowinski<ref name="isthe"/>
|-
| M<sub>132049</sub>
| 512740276269...455730061311
|style="text-align:right;"| 39,751
| 1983
| David Slowinski<ref name="isthe"/>
|-
| M<sub>216091</sub>
| 746093103064...103815528447
|style="text-align:right;"| 65,050
| 1985
| David Slowinski<ref name="isthe"/>
|-
| <math>391581 \times 2^{216193} - 1</math>
| 148140632376...836387377151
|style="text-align:right;"| 65,087
| 1989
| A group, "Amdahl Six": John Brown, [[Landon Curt Noll]], B. K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello.<ref>[https://www.jstor.org/stable/2324686 Letters to the Editor]. ''The American Mathematical Monthly'' 97, no. 3 (1990), p. 214. Accessed May 22, 2020.</ref><ref>[https://t5k.org/bios/code.php?code=Z Proof-code: Z], The [[Prime Pages]].</ref><br />Largest non-Mersenne prime that was the largest known prime when it was discovered.
|-
| M<sub>756839</sub>
| 174135906820...328544677887
|style="text-align:right;"| 227,832
| 1992
| David Slowinski and [[Paul Gage]]<ref name="isthe"/>
|-
| M<sub>859433</sub>
| 129498125604...243500142591
|style="text-align:right;"| 258,716
| 1994
| David Slowinski and Paul Gage<ref name="isthe"/>
|-
| M<sub>1257787</sub>
| 412245773621...976089366527
|style="text-align:right;"| 378,632
| 1996
| David Slowinski and Paul Gage<ref name="isthe"/>
|-
| M<sub>1398269</sub>
| 814717564412...868451315711
|style="text-align:right;"| 420,921
| 1996
| [[GIMPS]], Joel Armengaud
|-
| M<sub>2976221</sub>
| 623340076248...743729201151
|style="text-align:right;"| 895,932
| 1997
| [[GIMPS]], Gordon Spence
|-
| M<sub>3021377</sub>
| 127411683030...973024694271
|style="text-align:right;"| 909,526
| 1998
| [[GIMPS]], Roland Clarkson
|-
| M<sub>6972593</sub>
| 437075744127...142924193791
|style="text-align:right;"| 2,098,960
| 1999
| [[GIMPS]], Nayan Hajratwala
|-
| M<sub>13466917</sub>
| 924947738006...470256259071
|style="text-align:right;"| 4,053,946
| 2001
| [[GIMPS]], Michael Cameron
|-
| M<sub>20996011</sub>
| 125976895450...762855682047
|style="text-align:right;"| 6,320,430
| 2003
| [[GIMPS]], Michael Shafer
|-
| M<sub>24036583</sub>
|299410429404...882733969407
|style="text-align:right;"| 7,235,733
| 2004
| [[GIMPS]], Josh Findley
|-
| M<sub>25964951</sub>
| 122164630061...280577077247
|style="text-align:right;"| 7,816,230
| 2005
| [[GIMPS]], Martin Nowak
|-
| M<sub>30402457</sub>
| 315416475618...411652943871
|style="text-align:right;"| 9,152,052
| 2005
| [[GIMPS]], [[University of Central Missouri]] professors [[Curtis Cooper (mathematician)|Curtis Cooper]] and Steven Boone
|-
| M<sub>32582657</sub>
| 124575026015...154053967871
|style="text-align:right;"| 9,808,358
| 2006
| [[GIMPS]], [[Curtis Cooper (mathematician)|Curtis Cooper]] and Steven Boone
|-
| M<sub>43112609</sub>
| 316470269330...166697152511
|style="text-align:right;"| 12,978,189
| 2008
| [[GIMPS]], Edson Smith
|-
| M<sub>57885161</sub>
| 581887266232...071724285951
|style="text-align:right;"| 17,425,170
| 2013
| [[GIMPS]], [[Curtis Cooper (mathematician)|Curtis Cooper]]
|-
| M<sub>74207281</sub>
| 300376418084...391086436351
|style="text-align:right;"| 22,338,618
| 2016
| [[GIMPS]], [[Curtis Cooper (mathematician)|Curtis Cooper]]
|-
| M<sub>77232917</sub>
| 467333183359...069762179071
|style="text-align:right;"| 23,249,425
| 2017
| [[GIMPS]], Jonathan Pace
|-
| M<sub>82589933</sub>
| 148894445742...325217902591
|style="text-align:right;"| 24,862,048
| 2018
| [[GIMPS]], Patrick Laroche
|-
|}
[[GIMPS]] found the fifteen latest records (all of them Mersenne primes) on ordinary computers operated by participants around the world.
==The twenty largest known prime numbers==
A list of the 5,000 largest known primes is maintained by the [[PrimePages]],<ref>{{cite web|title=The Prime Database: The List of Largest Known Primes Home Page|url=https://t5k.org/primes/home.php|website=t5k.org/primes|access-date=19 March 2023}}</ref> of which the twenty largest are listed below.<ref>{{cite web|title=The Top Twenty: Largest Known Primes|url=https://t5k.org/top20/page.php?id=3|access-date=19 March 2023}}</ref>
{| class="wikitable sortable"
! Rank !!class="unsortable"| Number !! Discovered !! Digits !! Form !!class="unsortable"| Ref
|-
|style="text-align:right;"| 1
| 2<sup>82589933</sup> − 1
| 2018-12-07
|style="text-align:right;"| 24,862,048
|Mersenne
|<ref name="GIMPS-2018" />
|-
|style="text-align:right;"| 2
| 2<sup>77232917</sup> − 1
| 2017-12-26
|style="text-align:right;"| 23,249,425
|Mersenne
|<ref name="M77232917">{{cite web|title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>77,232,917</sup>-1|url=https://www.mersenne.org/primes/press/M77232917.html|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=3 January 2018}}</ref>
|-
|style="text-align:right;"| 3
| 2<sup>74207281</sup> − 1
| 2016-01-07
|style="text-align:right;"| 22,338,618
|Mersenne
|<ref name="M74207281">{{cite web|title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>74,207,281</sup>-1|url=https://www.mersenne.org/primes/?press=M74207281|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017}}</ref>
|-
|style="text-align:right;"| 4
| 2<sup>57885161</sup> − 1
| 2013-01-25
|style="text-align:right;"| 17,425,170
|Mersenne
|<ref name="M57885161">{{cite web|title=GIMPS Discovers 48th Mersenne Prime, 2<sup>57,885,161</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M57885161|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=5 February 2013}}</ref>
|-
|style="text-align:right;"| 5
| 2<sup>[[43,112,609 (number)|43112609]]</sup> − 1
| 2008-08-23
|style="text-align:right;"| 12,978,189
|Mersenne
| <ref name="M43112609">{{cite web|title=GIMPS Discovers 45th and 46th Mersenne Primes, 2<sup>43,112,609</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M43112609|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=15 September 2008}}</ref>
|-
|style="text-align:right;"| 6
| 2<sup>42643801</sup> − 1
| 2009-06-04
|style="text-align:right;"| 12,837,064
|Mersenne
| <ref name="M42643801">{{cite web|title=GIMPS Discovers 47th Mersenne Prime, 2<sup>42,643,801</sup>-1 is newest, but not the largest, known Mersenne Prime.|url=https://www.mersenne.org/primes/?press=M42643801|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=12 April 2009}}</ref>
|-
|style="text-align:right;"| 7
| [[Cyclotomic polynomial|Φ<sub>3</sub>]](−516693<sup>1048576</sup>)
| 2023-10-02
|style="text-align:right;"| 11,981,518
| [[Unique prime|Generalized unique]]
| <ref>{{cite web |title=PrimePage Primes: Phi(3, - 516693^1048576) |url=https://t5k.org/primes/page.php?id=136490 |website=t5k.org}}</ref>
|-
|style="text-align:right;"| 8
| Φ<sub>3</sub>(−465859<sup>1048576</sup>)
| 2023-05-31
|style="text-align:right;"| 11,887,192
| Generalized unique
| <ref>{{cite web |title=PrimePage Primes: Phi(3, - 465859^1048576) |url=https://t5k.org/primes/page.php?id=136107 |website=t5k.org}}</ref>
|-
|style="text-align:right;"| 9
| 2<sup>37156667</sup> − 1
| 2008-09-06
|style="text-align:right;"| 11,185,272
|Mersenne
| <ref name="M43112609"/>
|-
|style="text-align:right;"| 10
| 2<sup>32582657</sup> − 1
| 2006-09-04
|style="text-align:right;"| 9,808,358
|Mersenne
| <ref name="M32582657">{{cite web|title=GIMPS Discovers 44th Mersenne Prime, 2<sup>32,582,657</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M32582657|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=11 September 2006}}</ref>
|-
|style="text-align:right;"| 11
| 10223 × 2<sup>31172165</sup> + 1
| 2016-10-31
|style="text-align:right;"| 9,383,761
|[[Proth prime|Proth]]
| <ref name="SOB31172165">{{cite web|title=PrimeGrid's Seventeen or Bust Subproject|url=http://www.primegrid.com/download/SOB-31172165.pdf|website=primegrid.com|publisher=[[PrimeGrid]]|access-date=30 September 2017}}</ref>
|-
|style="text-align:right;"| 12
| 2<sup>30402457</sup> − 1
| 2005-12-15
|style="text-align:right;"| 9,152,052
|Mersenne
| <ref name="M30402457">{{cite web|title=GIMPS Discovers 43rd Mersenne Prime, 2<sup>30,402,457</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M30402457|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=24 December 2005}}</ref>
|-
|style="text-align:right;"| 13
| 2<sup>25964951</sup> − 1
| 2005-02-18
|style="text-align:right;"| 7,816,230
|Mersenne
| <ref name="M25964951">{{cite web|title=GIMPS Discovers 42nd Mersenne Prime, 2<sup>25,964,951</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M25964951|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=27 February 2005}}</ref>
|-
|style="text-align:right;"| 14
| 2<sup>24036583</sup> − 1
| 2004-05-15
|style="text-align:right;"| 7,235,733
|Mersenne
| <ref name="M24036583">{{cite web|title=GIMPS Discovers 41st Mersenne Prime, 2<sup>24,036,583</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M24036583|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=28 May 2004}}</ref>
|-
|style="text-align:right;"| 15
| 1963736<sup>1048576</sup> + 1
| 2022-09-24
|style="text-align:right;"| 6,598,776
|[[Fermat number#Generalized Fermat numbers|Generalized Fermat]]
| <ref>{{cite web|title=PrimeGrid's Generalized Fermat Prime Search|url=https://www.primegrid.com/download/GFN-1963736_1048576.pdf|website=primegrid.com|publisher=[[PrimeGrid]]|access-date=7 October 2022}}</ref>
|-
|style="text-align:right;"| 16
| 1951734<sup>1048576</sup> + 1
| 2022-08-09
|style="text-align:right;"| 6,595,985
|Generalized Fermat
| <ref>{{cite web|title=PrimeGrid's Generalized Fermat Prime Search|url=https://www.primegrid.com/download/GFN-1951734_1048576.pdf|website=primegrid.com|publisher=[[PrimeGrid]]|access-date=17 September 2022}}</ref>
|-
|style="text-align:right;"| 17
| 202705 × 2<sup>21320516</sup> + 1
| 2021-12-01
|style="text-align:right;"| 6,418,121
|Proth
| <ref>{{cite web|title=PrimeGrid's Extended Sierpinski Problem Prime Search|url=http://www.primegrid.com/download/ESP-202705.pdf|website=primegrid.com|publisher=[[PrimeGrid]]|access-date=28 December 2021}}</ref>
|-
|style="text-align:right;"| 18
| 2<sup>20996011</sup> − 1
| 2003-11-17
|style="text-align:right;"| 6,320,430
|Mersenne
| <ref name="M20996011">{{cite web|title=GIMPS Discovers 40th Mersenne Prime, 2<sup>20,996,011</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M20996011|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=2 December 2003}}</ref>
|-
|style="text-align:right;"| 19
| 1059094<sup>1048576</sup> + 1
| 2018-10-31
|style="text-align:right;"| 6,317,602
|Generalized Fermat
| <ref>{{cite web |title=PrimeGrid's Generalized Fermat Prime Search |url=https://www.primegrid.com/download/GFN-1059094_1048576.pdf |access-date=7 November 2018 |website=primegrid.com |publisher=[[PrimeGrid]]}}</ref>
|-
|style="text-align:right;"| 20
| 3 × 2<sup>20928756</sup> − 1
| 2023-07-05
|style="text-align:right;"| 6,300,184
|[[Thabit number|Thabit]]
| <ref>{{cite web |title=PrimeGrid's 321 Prime Search |url=https://www.primegrid.com/download/321-20928756.pdf |access-date=17 July 2023 |website=primegrid.com |publisher=[[PrimeGrid]]}}</ref>
|-
|}
==See also==
* [[List of largest known primes and probable primes]]
==References==
{{Reflist}}
==External links==
*[https://www.mersenne.org/primes/?press=M82589933 Press release about the largest known prime 2<sup>82,589,933</sup>−1]
*[https://www.mersenne.org/primes/?press=M77232917 Press release about the former largest known prime 2<sup>77,232,917</sup>−1]
*[https://www.mersenne.org/primes/?press=M74207281 Press release about the former largest known prime 2<sup>74,207,281</sup>−1]
{{Prime number classes}}
{{Large numbers}}
[[Category:Prime numbers]]
[[Category:Large integers]]
[[Category:World records|Prime number]]
[[Category:Largest things]]
[[Category:Great Internet Mersenne Prime Search]]
[[Category:Mersenne primes]]' |
New page wikitext, after the edit (new_wikitext ) | '{{short description|none}}
The '''largest known prime number''' is {{nowrap|2<sup>82,589,933</sup> − 1}}, a number which has 24,862,048 digits when written in [[base 10]]. It was found um what the sigma computer volunteered by Patrick Laroche of the [[Great Internet Mersenne Prime Search]] (GIMPS) in 2018.<ref name="GIMPS-2018">{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}</ref>
[[File:Digits in largest prime found as a function of time.svg|thumb|400px|A 2020 plot of the number of digits in the largest known prime by year, since the electronic computer. The vertical scale is [[logarithmic scale|logarithmic]].]]
A [[prime number]] is a [[natural number]] greater than 1 with no [[divisor]]s other than 1 and itself. According to [[Euclid's theorem]] there are infinitely many prime numbers, so there is no largest prime.
Many of the largest known primes are [[Mersenne prime]]s, numbers that are one less than a power of two, because they can utilize a [[Lucas–Lehmer primality test| specialized primality test]] that is faster than the general one. {{As of|2023|June}}, the six largest known primes are Mersenne primes.<ref>{{cite web |url=https://t5k.org/primes/search.php?Number=100 |title=The largest known primes – Database Search Output |publisher=Prime Pages |access-date=19 March 2023}}</ref> The last seventeen record primes were Mersenne primes.<ref name="computer history">{{cite web |url=http://t5k.org/notes/by_year.html |title=The Largest Known Prime by Year: A Brief History |first1=Chris |last1=Caldwell |publisher=Prime Pages |access-date=19 March 2023}}</ref><ref>The last non-Mersenne to be the largest known prime, was [http://t5k.org/primes/page.php?id=390 391,581 ⋅ 2<sup>216,193</sup> − 1]; see also [http://t5k.org/notes/by_year.html The Largest Known Prime by year: A Brief History] originally by Caldwell.</ref> The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2''<sup>k</sup>'' − 1 is simply ''k'' ones.<ref>{{Cite web|url=http://www.personal.psu.edu/sxt104/class/Math140H/PerfectNum.html|title=Perfect Numbers|website=Penn State University|access-date=6 October 2019|quote=An interesting side note is about the binary representations of those numbers...}}</ref>
==Current record==
The record is currently held by {{nowrap|2<sup>82,589,933</sup> − 1}} with 24,862,048 digits, found by [[Great Internet Mersenne Prime Search|GIMPS]] in December 2018.<ref name="GIMPS-2018">{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}</ref> The first and last 120 digits of its value are shown below:
{{quote|148894445742041325547806458472397916603026273992795324185271289425213239361064475310309971132180337174752834401423587560 ...
(24,861,808 digits skipped)
... 062107557947958297531595208807192693676521782184472526640076912114355308311969487633766457823695074037951210325217902591<ref>{{Cite web|url=https://www.mersenne.org/primes/press/M82589933.html|title = 51st Known Mersenne Prime Discovered}}</ref>
|sign=|source=|style=word-wrap: break-word}}
{{as of|2024|2}}, this prime has held the record for more than 5 years, longer than any other prime since M<sub>19937</sub> (which held the record for 7 years from 1971 to 1978).
==Prizes==
There are several prizes offered by the [[Electronic Frontier Foundation]] (EFF) for record primes.<ref name="prizes" /> A prime with one million digits was found in 1999, earning the discoverer a US$50,000 prize.<ref>Electronic Frontier Foundation, [https://www.eff.org/press/releases/big-prime-nets-big-prize Big Prime Nets Big Prize].</ref> In 2008, a ten-million digit prime won a US$100,000 prize and a [[Cooperative Computing Award]] from the EFF.<ref name="prizes">{{cite web |url=https://www.eff.org/press/archives/2009/10/14-0 |title=Record 12-Million-Digit Prime Number Nets $100,000 Prize |date=October 14, 2009 |work=Electronic Frontier Foundation |publisher=[[Electronic Frontier Foundation]] |access-date=November 26, 2011 }}</ref> ''[[Time (magazine)|Time]]'' called this prime the 29th top invention of 2008.<ref name="invention">{{cite news |url=http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html |archive-url=https://web.archive.org/web/20081102044641/http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html |url-status=dead |archive-date=November 2, 2008 |title=Best Inventions of 2008 - 29. The 46th Mersenne Prime |magazine=Time |publisher=[[Time Inc]] |access-date=January 17, 2012 |date=October 29, 2008}}</ref>
Both of these primes were discovered through the [[Great Internet Mersenne Prime Search]] (GIMPS), which coordinates long-range search efforts among tens of thousands of computers and thousands of volunteers. The $50,000 prize went to the discoverer and the $100,000 prize went to GIMPS. GIMPS will split the US$150,000 prize for the first prime of over 100 million digits with the winning participant. A further prize is offered for the first prime with at least one billion digits.<ref name="prizes" />
GIMPS also offers a US$3,000 research discovery award for participants who discover a new Mersenne prime of less than 100 million digits.<ref>{{cite web |title=GIMPS by Mersenne Research, Inc. |url=https://www.mersenne.org/legal/ |access-date=21 November 2022 |website=mersenne.org}}</ref>
==History of largest known prime numbers==
[[File:MersennePrimeStamp.gif|thumb|right|287px|Commemorative postmark used by the [[University of Illinois at Urbana–Champaign|UIUC]] Math Department after proving that M<sub>11213</sub> is prime]]
The following table lists the progression of the largest known prime number in ascending order.<ref name="computer history" /> Here {{nowrap|M<sub>''p''</sub> {{=}} 2<sup>''p''</sup> − 1}} is the Mersenne number with exponent ''p'', where ''p'' is a prime number. The longest record-holder known was {{nowrap|M<sub>19</sub> {{=}} 524,287}}, which was the largest known prime for 144 years. No records are known prior to 1456.
{{clear}}
{| class="wikitable sortable" border="1"
|-
! Number
! Decimal expansion<br/>(partial for numbers > M<sub>1000</sub>)
! Digits
! Year found
! Discoverer<br/>
|-
| M<sub>13</sub>
|style="text-align:right;"| 8,191
|style="text-align:right;"| 4
| 1456
| Anonymous
|-
| M<sub>17</sub>
|style="text-align:right;"| 131,071
|style="text-align:right;"| 6
| 1588
| [[Pietro Cataldi]]
|-
| M<sub>19</sub>
|style="text-align:right;"| 524,287
|style="text-align:right;"| 6
| 1588
| Pietro Cataldi
|-
| <math>\tfrac{2^{32}+1}{641}</math>
|style="text-align:right;"| 6,700,417
|style="text-align:right;"| 7
| 1732
| [[Leonhard Euler]]?<br>Euler did not explicitly publish the primality of 6,700,417, but the techniques he had used to factorise 2<sup>32</sup> + 1 meant that he had already done most of the work needed to prove this, and some experts believe he knew of it.<ref>{{Cite book|url=https://books.google.com/books?id=3c6iBQAAQBAJ&pg=PA43|title = How Euler Did Even More|isbn = 9780883855843|last1 = Edward Sandifer|first1 = C.|date = 19 November 2014| publisher=The Mathematical Association of America }}</ref>
|-
| M<sub>31</sub>
|style="text-align:right;"| [[2,147,483,647]]
|style="text-align:right;"| 10
| 1772
| Leonhard Euler
|-
| <math>\tfrac{10^{18}+1}{1000001}</math>
|style="text-align:right;"| 999,999,000,001
|style="text-align:right;"| 12
| 1851
| Included (but question-marked) in a list of primes by Looff. Given his uncertainty, some do not include this as a record.
|-
| <math>\tfrac{2^{64}+1}{274177}</math>
|style="text-align:right;"| 67,280,421,310,721
|style="text-align:right;"| 14
| 1855
| [[Thomas Clausen (mathematician)|Thomas Clausen]] (but no proof was provided).
<!--|-
| [M<sub>59</sub>/179951]
|style="text-align:right;"| [3,203,431,780,337]
|style="text-align:right;"| [13]
| [1867]
| Landry. A record if the immediately preceding entry is excluded.-->
|-
| M<sub>127</sub>
|style="text-align:right;"| 170,141,183,460,469,<wbr/>231,731,687,303,715,<wbr/>884,105,727
|style="text-align:right;"| 39
| 1876
| [[Édouard Lucas]]
|-
| <math>\tfrac{2^{148}+1}{17}</math>
|style="text-align:right;"| 20,988,936,657,440,<wbr/>586,486,151,264,256,<wbr/>610,222,593,863,921
|style="text-align:right;"| 44
| 1951
| [[Aimé Ferrier]] with a mechanical calculator; the largest record not set by computer.
|-
| 180×(M<sub>127</sub>)<sup>2</sup>+1
|
521064401567922879406069432539<wbr />095585333589848390805645835218<wbr />3851018372555735221
|style="text-align:right;"| 79
| 1951
| [[J. C. P. Miller]] & [[David Wheeler (computer scientist)|D. J. Wheeler]]<ref>[[J. C. P. Miller|J. Miller]], [https://doi.org/10.1038/168838b0 Large Prime Numbers]. ''Nature'' 168, 838 (1951).</ref><br />Using [[University of Cambridge Mathematical Laboratory|Cambridge's]] [[Electronic delay storage automatic calculator|EDSAC]] computer
|-
| M<sub>521</sub>
|
686479766013060971498190079908<wbr />139321726943530014330540939446<wbr />345918554318339765605212255964<wbr />066145455497729631139148085803<wbr />712198799971664381257402829111<wbr />5057151
|style="text-align:right;"| 157
| 1952
| [[Raphael M. Robinson]]
|-
| M<sub>607</sub>
|
531137992816767098689588206552<wbr />468627329593117727031923199444<wbr />138200403559860852242739162502<wbr />265229285668889329486246501015<wbr />346579337652707239409519978766<wbr />587351943831270835393219031728127
|style="text-align:right;"| 183
| 1952
| Raphael M. Robinson
|-
| M<sub>1279</sub>
| 104079321946...703168729087
|style="text-align:right;"| 386
| 1952
| Raphael M. Robinson
|-
| M<sub>2203</sub>
| 147597991521...686697771007
|style="text-align:right;"| 664
| 1952
| Raphael M. Robinson
|-
| M<sub>2281</sub>
| 446087557183...418132836351
|style="text-align:right;"| 687
| 1952
| Raphael M. Robinson
|-
| M<sub>3217</sub>
| 259117086013...362909315071
|style="text-align:right;"| 969
| 1957
| [[Hans Riesel]]
|-
| M<sub>4423</sub>
| 285542542228...902608580607
|style="text-align:right;"| 1,332
| 1961
| [[Alexander Hurwitz]]
|-
| M<sub>9689</sub>
| 478220278805...826225754111
|style="text-align:right;"| 2,917
| 1963
| [[Donald B. Gillies]]
|-
| M<sub>9941</sub>
| 346088282490...883789463551
|style="text-align:right;"| 2,993
| 1963
| Donald B. Gillies
|-
| M<sub>11213</sub>
| 281411201369...087696392191
|style="text-align:right;"| 3,376
| 1963
| Donald B. Gillies
|-
| M<sub>19937</sub>
| 431542479738...030968041471
|style="text-align:right;"| 6,002
| 1971
| [[Bryant Tuckerman]]
|-
| M<sub>21701</sub>
| 448679166119...353511882751
|style="text-align:right;"| 6,533
| 1978
| Laura A. Nickel and [[Landon Curt Noll]]<ref name="isthe">[[Landon Curt Noll]], [http://www.isthe.com/chongo/tech/math/prime/prime_press.html Large Prime Number Found by SGI/Cray Supercomputer].</ref>
|-
| M<sub>23209</sub>
| 402874115778...523779264511
|style="text-align:right;"| 6,987
| 1979
| Landon Curt Noll<ref name="isthe"/>
|-
| M<sub>44497</sub>
| 854509824303...961011228671
|style="text-align:right;"| 13,395
| 1979
| [[David Slowinski]] and [[Harry L. Nelson]]<ref name="isthe"/>
|-
| M<sub>86243</sub>
| 536927995502...709433438207
|style="text-align:right;"| 25,962
| 1982
| David Slowinski<ref name="isthe"/>
|-
| M<sub>132049</sub>
| 512740276269...455730061311
|style="text-align:right;"| 39,751
| 1983
| David Slowinski<ref name="isthe"/>
|-
| M<sub>216091</sub>
| 746093103064...103815528447
|style="text-align:right;"| 65,050
| 1985
| David Slowinski<ref name="isthe"/>
|-
| <math>391581 \times 2^{216193} - 1</math>
| 148140632376...836387377151
|style="text-align:right;"| 65,087
| 1989
| A group, "Amdahl Six": John Brown, [[Landon Curt Noll]], B. K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello.<ref>[https://www.jstor.org/stable/2324686 Letters to the Editor]. ''The American Mathematical Monthly'' 97, no. 3 (1990), p. 214. Accessed May 22, 2020.</ref><ref>[https://t5k.org/bios/code.php?code=Z Proof-code: Z], The [[Prime Pages]].</ref><br />Largest non-Mersenne prime that was the largest known prime when it was discovered.
|-
| M<sub>756839</sub>
| 174135906820...328544677887
|style="text-align:right;"| 227,832
| 1992
| David Slowinski and [[Paul Gage]]<ref name="isthe"/>
|-
| M<sub>859433</sub>
| 129498125604...243500142591
|style="text-align:right;"| 258,716
| 1994
| David Slowinski and Paul Gage<ref name="isthe"/>
|-
| M<sub>1257787</sub>
| 412245773621...976089366527
|style="text-align:right;"| 378,632
| 1996
| David Slowinski and Paul Gage<ref name="isthe"/>
|-
| M<sub>1398269</sub>
| 814717564412...868451315711
|style="text-align:right;"| 420,921
| 1996
| [[GIMPS]], Joel Armengaud
|-
| M<sub>2976221</sub>
| 623340076248...743729201151
|style="text-align:right;"| 895,932
| 1997
| [[GIMPS]], Gordon Spence
|-
| M<sub>3021377</sub>
| 127411683030...973024694271
|style="text-align:right;"| 909,526
| 1998
| [[GIMPS]], Roland Clarkson
|-
| M<sub>6972593</sub>
| 437075744127...142924193791
|style="text-align:right;"| 2,098,960
| 1999
| [[GIMPS]], Nayan Hajratwala
|-
| M<sub>13466917</sub>
| 924947738006...470256259071
|style="text-align:right;"| 4,053,946
| 2001
| [[GIMPS]], Michael Cameron
|-
| M<sub>20996011</sub>
| 125976895450...762855682047
|style="text-align:right;"| 6,320,430
| 2003
| [[GIMPS]], Michael Shafer
|-
| M<sub>24036583</sub>
|299410429404...882733969407
|style="text-align:right;"| 7,235,733
| 2004
| [[GIMPS]], Josh Findley
|-
| M<sub>25964951</sub>
| 122164630061...280577077247
|style="text-align:right;"| 7,816,230
| 2005
| [[GIMPS]], Martin Nowak
|-
| M<sub>30402457</sub>
| 315416475618...411652943871
|style="text-align:right;"| 9,152,052
| 2005
| [[GIMPS]], [[University of Central Missouri]] professors [[Curtis Cooper (mathematician)|Curtis Cooper]] and Steven Boone
|-
| M<sub>32582657</sub>
| 124575026015...154053967871
|style="text-align:right;"| 9,808,358
| 2006
| [[GIMPS]], [[Curtis Cooper (mathematician)|Curtis Cooper]] and Steven Boone
|-
| M<sub>43112609</sub>
| 316470269330...166697152511
|style="text-align:right;"| 12,978,189
| 2008
| [[GIMPS]], Edson Smith
|-
| M<sub>57885161</sub>
| 581887266232...071724285951
|style="text-align:right;"| 17,425,170
| 2013
| [[GIMPS]], [[Curtis Cooper (mathematician)|Curtis Cooper]]
|-
| M<sub>74207281</sub>
| 300376418084...391086436351
|style="text-align:right;"| 22,338,618
| 2016
| [[GIMPS]], [[Curtis Cooper (mathematician)|Curtis Cooper]]
|-
| M<sub>77232917</sub>
| 467333183359...069762179071
|style="text-align:right;"| 23,249,425
| 2017
| [[GIMPS]], Jonathan Pace
|-
| M<sub>82589933</sub>
| 148894445742...325217902591
|style="text-align:right;"| 24,862,048
| 2018
| [[GIMPS]], Patrick Laroche
|-
|}
[[GIMPS]] found the fifteen latest records (all of them Mersenne primes) on ordinary computers operated by participants around the world.
==The twenty largest known prime numbers==
A list of the 5,000 largest known primes is maintained by the [[PrimePages]],<ref>{{cite web|title=The Prime Database: The List of Largest Known Primes Home Page|url=https://t5k.org/primes/home.php|website=t5k.org/primes|access-date=19 March 2023}}</ref> of which the twenty largest are listed below.<ref>{{cite web|title=The Top Twenty: Largest Known Primes|url=https://t5k.org/top20/page.php?id=3|access-date=19 March 2023}}</ref>
{| class="wikitable sortable"
! Rank !!class="unsortable"| Number !! Discovered !! Digits !! Form !!class="unsortable"| Ref
|-
|style="text-align:right;"| 1
| 2<sup>82589933</sup> − 1
| 2018-12-07
|style="text-align:right;"| 24,862,048
|Mersenne
|<ref name="GIMPS-2018" />
|-
|style="text-align:right;"| 2
| 2<sup>77232917</sup> − 1
| 2017-12-26
|style="text-align:right;"| 23,249,425
|Mersenne
|<ref name="M77232917">{{cite web|title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>77,232,917</sup>-1|url=https://www.mersenne.org/primes/press/M77232917.html|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=3 January 2018}}</ref>
|-
|style="text-align:right;"| 3
| 2<sup>74207281</sup> − 1
| 2016-01-07
|style="text-align:right;"| 22,338,618
|Mersenne
|<ref name="M74207281">{{cite web|title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>74,207,281</sup>-1|url=https://www.mersenne.org/primes/?press=M74207281|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017}}</ref>
|-
|style="text-align:right;"| 4
| 2<sup>57885161</sup> − 1
| 2013-01-25
|style="text-align:right;"| 17,425,170
|Mersenne
|<ref name="M57885161">{{cite web|title=GIMPS Discovers 48th Mersenne Prime, 2<sup>57,885,161</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M57885161|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=5 February 2013}}</ref>
|-
|style="text-align:right;"| 5
| 2<sup>[[43,112,609 (number)|43112609]]</sup> − 1
| 2008-08-23
|style="text-align:right;"| 12,978,189
|Mersenne
| <ref name="M43112609">{{cite web|title=GIMPS Discovers 45th and 46th Mersenne Primes, 2<sup>43,112,609</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M43112609|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=15 September 2008}}</ref>
|-
|style="text-align:right;"| 6
| 2<sup>42643801</sup> − 1
| 2009-06-04
|style="text-align:right;"| 12,837,064
|Mersenne
| <ref name="M42643801">{{cite web|title=GIMPS Discovers 47th Mersenne Prime, 2<sup>42,643,801</sup>-1 is newest, but not the largest, known Mersenne Prime.|url=https://www.mersenne.org/primes/?press=M42643801|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=12 April 2009}}</ref>
|-
|style="text-align:right;"| 7
| [[Cyclotomic polynomial|Φ<sub>3</sub>]](−516693<sup>1048576</sup>)
| 2023-10-02
|style="text-align:right;"| 11,981,518
| [[Unique prime|Generalized unique]]
| <ref>{{cite web |title=PrimePage Primes: Phi(3, - 516693^1048576) |url=https://t5k.org/primes/page.php?id=136490 |website=t5k.org}}</ref>
|-
|style="text-align:right;"| 8
| Φ<sub>3</sub>(−465859<sup>1048576</sup>)
| 2023-05-31
|style="text-align:right;"| 11,887,192
| Generalized unique
| <ref>{{cite web |title=PrimePage Primes: Phi(3, - 465859^1048576) |url=https://t5k.org/primes/page.php?id=136107 |website=t5k.org}}</ref>
|-
|style="text-align:right;"| 9
| 2<sup>37156667</sup> − 1
| 2008-09-06
|style="text-align:right;"| 11,185,272
|Mersenne
| <ref name="M43112609"/>
|-
|style="text-align:right;"| 10
| 2<sup>32582657</sup> − 1
| 2006-09-04
|style="text-align:right;"| 9,808,358
|Mersenne
| <ref name="M32582657">{{cite web|title=GIMPS Discovers 44th Mersenne Prime, 2<sup>32,582,657</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M32582657|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=11 September 2006}}</ref>
|-
|style="text-align:right;"| 11
| 10223 × 2<sup>31172165</sup> + 1
| 2016-10-31
|style="text-align:right;"| 9,383,761
|[[Proth prime|Proth]]
| <ref name="SOB31172165">{{cite web|title=PrimeGrid's Seventeen or Bust Subproject|url=http://www.primegrid.com/download/SOB-31172165.pdf|website=primegrid.com|publisher=[[PrimeGrid]]|access-date=30 September 2017}}</ref>
|-
|style="text-align:right;"| 12
| 2<sup>30402457</sup> − 1
| 2005-12-15
|style="text-align:right;"| 9,152,052
|Mersenne
| <ref name="M30402457">{{cite web|title=GIMPS Discovers 43rd Mersenne Prime, 2<sup>30,402,457</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M30402457|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=24 December 2005}}</ref>
|-
|style="text-align:right;"| 13
| 2<sup>25964951</sup> − 1
| 2005-02-18
|style="text-align:right;"| 7,816,230
|Mersenne
| <ref name="M25964951">{{cite web|title=GIMPS Discovers 42nd Mersenne Prime, 2<sup>25,964,951</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M25964951|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=27 February 2005}}</ref>
|-
|style="text-align:right;"| 14
| 2<sup>24036583</sup> − 1
| 2004-05-15
|style="text-align:right;"| 7,235,733
|Mersenne
| <ref name="M24036583">{{cite web|title=GIMPS Discovers 41st Mersenne Prime, 2<sup>24,036,583</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M24036583|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=28 May 2004}}</ref>
|-
|style="text-align:right;"| 15
| 1963736<sup>1048576</sup> + 1
| 2022-09-24
|style="text-align:right;"| 6,598,776
|[[Fermat number#Generalized Fermat numbers|Generalized Fermat]]
| <ref>{{cite web|title=PrimeGrid's Generalized Fermat Prime Search|url=https://www.primegrid.com/download/GFN-1963736_1048576.pdf|website=primegrid.com|publisher=[[PrimeGrid]]|access-date=7 October 2022}}</ref>
|-
|style="text-align:right;"| 16
| 1951734<sup>1048576</sup> + 1
| 2022-08-09
|style="text-align:right;"| 6,595,985
|Generalized Fermat
| <ref>{{cite web|title=PrimeGrid's Generalized Fermat Prime Search|url=https://www.primegrid.com/download/GFN-1951734_1048576.pdf|website=primegrid.com|publisher=[[PrimeGrid]]|access-date=17 September 2022}}</ref>
|-
|style="text-align:right;"| 17
| 202705 × 2<sup>21320516</sup> + 1
| 2021-12-01
|style="text-align:right;"| 6,418,121
|Proth
| <ref>{{cite web|title=PrimeGrid's Extended Sierpinski Problem Prime Search|url=http://www.primegrid.com/download/ESP-202705.pdf|website=primegrid.com|publisher=[[PrimeGrid]]|access-date=28 December 2021}}</ref>
|-
|style="text-align:right;"| 18
| 2<sup>20996011</sup> − 1
| 2003-11-17
|style="text-align:right;"| 6,320,430
|Mersenne
| <ref name="M20996011">{{cite web|title=GIMPS Discovers 40th Mersenne Prime, 2<sup>20,996,011</sup>-1 is now the Largest Known Prime.|url=https://www.mersenne.org/primes/?press=M20996011|website=mersenne.org|publisher=[[Great Internet Mersenne Prime Search]]|access-date=29 September 2017|date=2 December 2003}}</ref>
|-
|style="text-align:right;"| 19
| 1059094<sup>1048576</sup> + 1
| 2018-10-31
|style="text-align:right;"| 6,317,602
|Generalized Fermat
| <ref>{{cite web |title=PrimeGrid's Generalized Fermat Prime Search |url=https://www.primegrid.com/download/GFN-1059094_1048576.pdf |access-date=7 November 2018 |website=primegrid.com |publisher=[[PrimeGrid]]}}</ref>
|-
|style="text-align:right;"| 20
| 3 × 2<sup>20928756</sup> − 1
| 2023-07-05
|style="text-align:right;"| 6,300,184
|[[Thabit number|Thabit]]
| <ref>{{cite web |title=PrimeGrid's 321 Prime Search |url=https://www.primegrid.com/download/321-20928756.pdf |access-date=17 July 2023 |website=primegrid.com |publisher=[[PrimeGrid]]}}</ref>
|-
|}
==See also==
* [[List of largest known primes and probable primes]]
==References==
{{Reflist}}
==External links==
*[https://www.mersenne.org/primes/?press=M82589933 Press release about the largest known prime 2<sup>82,589,933</sup>−1]
*[https://www.mersenne.org/primes/?press=M77232917 Press release about the former largest known prime 2<sup>77,232,917</sup>−1]
*[https://www.mersenne.org/primes/?press=M74207281 Press release about the former largest known prime 2<sup>74,207,281</sup>−1]
{{Prime number classes}}
{{Large numbers}}
[[Category:Prime numbers]]
[[Category:Large integers]]
[[Category:World records|Prime number]]
[[Category:Largest things]]
[[Category:Great Internet Mersenne Prime Search]]
[[Category:Mersenne primes]]' |
Unified diff of changes made by edit (edit_diff ) | '@@ -1,4 +1,4 @@
{{short description|none}}
-The '''largest known prime number''' is {{nowrap|2<sup>82,589,933</sup> − 1}}, a number which has 24,862,048 digits when written in [[base 10]]. It was found via a computer volunteered by Patrick Laroche of the [[Great Internet Mersenne Prime Search]] (GIMPS) in 2018.<ref name="GIMPS-2018">{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}</ref>
+The '''largest known prime number''' is {{nowrap|2<sup>82,589,933</sup> − 1}}, a number which has 24,862,048 digits when written in [[base 10]]. It was found um what the sigma computer volunteered by Patrick Laroche of the [[Great Internet Mersenne Prime Search]] (GIMPS) in 2018.<ref name="GIMPS-2018">{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}</ref>
[[File:Digits in largest prime found as a function of time.svg|thumb|400px|A 2020 plot of the number of digits in the largest known prime by year, since the electronic computer. The vertical scale is [[logarithmic scale|logarithmic]].]]
' |
New page size (new_size ) | 24006 |
Old page size (old_size ) | 23994 |
Size change in edit (edit_delta ) | 12 |
Lines added in edit (added_lines ) | [
0 => 'The '''largest known prime number''' is {{nowrap|2<sup>82,589,933</sup> − 1}}, a number which has 24,862,048 digits when written in [[base 10]]. It was found um what the sigma computer volunteered by Patrick Laroche of the [[Great Internet Mersenne Prime Search]] (GIMPS) in 2018.<ref name="GIMPS-2018">{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}</ref>'
] |
Lines removed in edit (removed_lines ) | [
0 => 'The '''largest known prime number''' is {{nowrap|2<sup>82,589,933</sup> − 1}}, a number which has 24,862,048 digits when written in [[base 10]]. It was found via a computer volunteered by Patrick Laroche of the [[Great Internet Mersenne Prime Search]] (GIMPS) in 2018.<ref name="GIMPS-2018">{{cite web |title=GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1 |url=https://www.mersenne.org/primes/press/M82589933.html |date=21 December 2018 |work=Mersenne Research, Inc. |access-date=21 December 2018 }}</ref>'
] |
All external links added in the edit (added_links ) | [] |
All external links removed in the edit (removed_links ) | [] |
All external links in the new text (all_links ) | [
0 => 'https://www.mersenne.org/primes/press/M82589933.html',
1 => 'https://t5k.org/primes/search.php?Number=100',
2 => 'http://t5k.org/notes/by_year.html',
3 => 'http://t5k.org/primes/page.php?id=390',
4 => 'http://www.personal.psu.edu/sxt104/class/Math140H/PerfectNum.html',
5 => 'https://www.eff.org/press/archives/2009/10/14-0',
6 => 'https://www.eff.org/press/releases/big-prime-nets-big-prize',
7 => 'https://web.archive.org/web/20081102044641/http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html',
8 => 'http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html',
9 => 'https://www.mersenne.org/legal/',
10 => 'https://books.google.com/books?id=3c6iBQAAQBAJ&pg=PA43',
11 => 'https://doi.org/10.1038/168838b0',
12 => 'http://www.isthe.com/chongo/tech/math/prime/prime_press.html',
13 => 'https://www.jstor.org/stable/2324686',
14 => 'https://t5k.org/bios/code.php?code=Z',
15 => 'https://t5k.org/primes/home.php',
16 => 'https://t5k.org/top20/page.php?id=3',
17 => 'https://www.mersenne.org/primes/press/M77232917.html',
18 => 'https://www.mersenne.org/primes/?press=M74207281',
19 => 'https://www.mersenne.org/primes/?press=M57885161',
20 => 'https://www.mersenne.org/primes/?press=M43112609',
21 => 'https://www.mersenne.org/primes/?press=M42643801',
22 => 'https://t5k.org/primes/page.php?id=136490',
23 => 'https://t5k.org/primes/page.php?id=136107',
24 => 'https://www.mersenne.org/primes/?press=M32582657',
25 => 'http://www.primegrid.com/download/SOB-31172165.pdf',
26 => 'https://www.mersenne.org/primes/?press=M30402457',
27 => 'https://www.mersenne.org/primes/?press=M25964951',
28 => 'https://www.mersenne.org/primes/?press=M24036583',
29 => 'https://www.primegrid.com/download/GFN-1963736_1048576.pdf',
30 => 'https://www.primegrid.com/download/GFN-1951734_1048576.pdf',
31 => 'http://www.primegrid.com/download/ESP-202705.pdf',
32 => 'https://www.mersenne.org/primes/?press=M20996011',
33 => 'https://www.primegrid.com/download/GFN-1059094_1048576.pdf',
34 => 'https://www.primegrid.com/download/321-20928756.pdf',
35 => 'https://www.mersenne.org/primes/?press=M82589933',
36 => 'https://www.mersenne.org/primes/?press=M77232917'
] |
Links in the page, before the edit (old_links ) | [
0 => 'https://www.eff.org/press/archives/2009/10/14-0',
1 => 'http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html',
2 => 'https://www.eff.org/press/releases/big-prime-nets-big-prize',
3 => 'https://www.mersenne.org/primes/?press=M74207281',
4 => 'https://www.mersenne.org/primes/?press=M57885161',
5 => 'https://www.mersenne.org/primes/?press=M43112609',
6 => 'https://www.mersenne.org/primes/?press=M42643801',
7 => 'https://www.mersenne.org/primes/?press=M32582657',
8 => 'http://www.primegrid.com/download/SOB-31172165.pdf',
9 => 'https://www.mersenne.org/primes/?press=M30402457',
10 => 'https://www.mersenne.org/primes/?press=M25964951',
11 => 'https://www.mersenne.org/primes/?press=M24036583',
12 => 'https://www.mersenne.org/primes/?press=M20996011',
13 => 'https://www.mersenne.org/primes/press/M77232917.html',
14 => 'https://www.mersenne.org/primes/?press=M77232917',
15 => 'https://www.primegrid.com/download/GFN-1059094_1048576.pdf',
16 => 'https://www.mersenne.org/primes/?press=M82589933',
17 => 'https://www.jstor.org/stable/2324686',
18 => 'https://doi.org/10.1038/168838b0',
19 => 'http://www.isthe.com/chongo/tech/math/prime/prime_press.html',
20 => 'https://books.google.com/books?id=3c6iBQAAQBAJ&pg=PA43',
21 => 'https://web.archive.org/web/20081102044641/http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html',
22 => 'http://www.primegrid.com/download/ESP-202705.pdf',
23 => 'https://www.primegrid.com/download/GFN-1951734_1048576.pdf',
24 => 'https://www.primegrid.com/download/GFN-1963736_1048576.pdf',
25 => 'https://www.mersenne.org/legal/',
26 => 'http://www.personal.psu.edu/sxt104/class/Math140H/PerfectNum.html',
27 => 'https://t5k.org/primes/home.php',
28 => 'https://t5k.org/top20/page.php?id=3',
29 => 'https://t5k.org/primes/search.php?Number=100',
30 => 'http://t5k.org/notes/by_year.html',
31 => 'http://t5k.org/primes/page.php?id=390',
32 => 'https://t5k.org/bios/code.php?code=Z',
33 => 'https://t5k.org/primes/page.php?id=136107',
34 => 'https://www.primegrid.com/download/321-20928756.pdf',
35 => 'https://www.mersenne.org/primes/press/M82589933.html',
36 => 'https://t5k.org/primes/page.php?id=136490'
] |
Parsed HTML source of the new revision (new_html ) | '<div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>
The <b>largest known prime number</b> is <span class="nowrap">2<sup>82,589,933</sup> − 1</span>, a number which has 24,862,048 digits when written in <a href="/wiki/Base_10" class="mw-redirect" title="Base 10">base 10</a>. It was found um what the sigma computer volunteered by Patrick Laroche of the <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a> (GIMPS) in 2018.<sup id="cite_ref-GIMPS-2018_1-0" class="reference"><a href="#cite_note-GIMPS-2018-1">[1]</a></sup>
</p>
<figure typeof="mw:File/Thumb"><a href="/wiki/File:Digits_in_largest_prime_found_as_a_function_of_time.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Digits_in_largest_prime_found_as_a_function_of_time.svg/400px-Digits_in_largest_prime_found_as_a_function_of_time.svg.png" decoding="async" width="400" height="302" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Digits_in_largest_prime_found_as_a_function_of_time.svg/600px-Digits_in_largest_prime_found_as_a_function_of_time.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Digits_in_largest_prime_found_as_a_function_of_time.svg/800px-Digits_in_largest_prime_found_as_a_function_of_time.svg.png 2x" data-file-width="540" data-file-height="408" /></a><figcaption>A 2020 plot of the number of digits in the largest known prime by year, since the electronic computer. The vertical scale is <a href="/wiki/Logarithmic_scale" title="Logarithmic scale">logarithmic</a>.</figcaption></figure>
<p>A <a href="/wiki/Prime_number" title="Prime number">prime number</a> is a <a href="/wiki/Natural_number" title="Natural number">natural number</a> greater than 1 with no <a href="/wiki/Divisor" title="Divisor">divisors</a> other than 1 and itself. According to <a href="/wiki/Euclid%27s_theorem" title="Euclid's theorem">Euclid's theorem</a> there are infinitely many prime numbers, so there is no largest prime.
</p><p>Many of the largest known primes are <a href="/wiki/Mersenne_prime" title="Mersenne prime">Mersenne primes</a>, numbers that are one less than a power of two, because they can utilize a <a href="/wiki/Lucas%E2%80%93Lehmer_primality_test" title="Lucas–Lehmer primality test"> specialized primality test</a> that is faster than the general one. As of June 2023<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Largest_known_prime_number&action=edit">[update]</a></sup>, the six largest known primes are Mersenne primes.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup> The last seventeen record primes were Mersenne primes.<sup id="cite_ref-computer_history_3-0" class="reference"><a href="#cite_note-computer_history-3">[3]</a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4">[4]</a></sup> The binary representation of any Mersenne prime is composed of all ones, since the binary form of 2<i><sup>k</sup></i> − 1 is simply <i>k</i> ones.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5">[5]</a></sup>
</p>
<div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Current_record"><span class="tocnumber">1</span> <span class="toctext">Current record</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="#Prizes"><span class="tocnumber">2</span> <span class="toctext">Prizes</span></a></li>
<li class="toclevel-1 tocsection-3"><a href="#History_of_largest_known_prime_numbers"><span class="tocnumber">3</span> <span class="toctext">History of largest known prime numbers</span></a></li>
<li class="toclevel-1 tocsection-4"><a href="#The_twenty_largest_known_prime_numbers"><span class="tocnumber">4</span> <span class="toctext">The twenty largest known prime numbers</span></a></li>
<li class="toclevel-1 tocsection-5"><a href="#See_also"><span class="tocnumber">5</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-6"><a href="#References"><span class="tocnumber">6</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-7"><a href="#External_links"><span class="tocnumber">7</span> <span class="toctext">External links</span></a></li>
</ul>
</div>
<h2><span class="mw-headline" id="Current_record">Current record</span><span class="mw-editsection">
<a role="button"
href="/w/index.php?title=Largest_known_prime_number&action=edit&section=1"title="Edit section: Current record"
class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet ">
<span class="minerva-icon minerva-icon--edit"></span>
<span>edit</span>
</a>
</span>
</h2>
<p>The record is currently held by <span class="nowrap">2<sup>82,589,933</sup> − 1</span> with 24,862,048 digits, found by <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">GIMPS</a> in December 2018.<sup id="cite_ref-GIMPS-2018_1-1" class="reference"><a href="#cite_note-GIMPS-2018-1">[1]</a></sup> The first and last 120 digits of its value are shown below:
</p>
<style data-mw-deduplicate="TemplateStyles:r1211633275">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequote .templatequotecite{line-height:1.5em;text-align:left;padding-left:1.6em;margin-top:0}</style><blockquote class="templatequote" style="word-wrap: break-word"><p>148894445742041325547806458472397916603026273992795324185271289425213239361064475310309971132180337174752834401423587560 ...
</p><p>(24,861,808 digits skipped)
</p><p> ... 062107557947958297531595208807192693676521782184472526640076912114355308311969487633766457823695074037951210325217902591<sup id="cite_ref-6" class="reference"><a href="#cite_note-6">[6]</a></sup>
</p>
</blockquote>
<p>As of February 2024<sup class="plainlinks noexcerpt noprint asof-tag update" style="display:none;"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Largest_known_prime_number&action=edit">[update]</a></sup>, this prime has held the record for more than 5 years, longer than any other prime since M<sub>19937</sub> (which held the record for 7 years from 1971 to 1978).
</p>
<h2><span class="mw-headline" id="Prizes">Prizes</span><span class="mw-editsection">
<a role="button"
href="/w/index.php?title=Largest_known_prime_number&action=edit&section=2"title="Edit section: Prizes"
class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet ">
<span class="minerva-icon minerva-icon--edit"></span>
<span>edit</span>
</a>
</span>
</h2>
<p>There are several prizes offered by the <a href="/wiki/Electronic_Frontier_Foundation" title="Electronic Frontier Foundation">Electronic Frontier Foundation</a> (EFF) for record primes.<sup id="cite_ref-prizes_7-0" class="reference"><a href="#cite_note-prizes-7">[7]</a></sup> A prime with one million digits was found in 1999, earning the discoverer a US$50,000 prize.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8">[8]</a></sup> In 2008, a ten-million digit prime won a US$100,000 prize and a <a href="/wiki/Cooperative_Computing_Award" class="mw-redirect" title="Cooperative Computing Award">Cooperative Computing Award</a> from the EFF.<sup id="cite_ref-prizes_7-1" class="reference"><a href="#cite_note-prizes-7">[7]</a></sup> <i><a href="/wiki/Time_(magazine)" title="Time (magazine)">Time</a></i> called this prime the 29th top invention of 2008.<sup id="cite_ref-invention_9-0" class="reference"><a href="#cite_note-invention-9">[9]</a></sup>
</p><p>Both of these primes were discovered through the <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a> (GIMPS), which coordinates long-range search efforts among tens of thousands of computers and thousands of volunteers. The $50,000 prize went to the discoverer and the $100,000 prize went to GIMPS. GIMPS will split the US$150,000 prize for the first prime of over 100 million digits with the winning participant. A further prize is offered for the first prime with at least one billion digits.<sup id="cite_ref-prizes_7-2" class="reference"><a href="#cite_note-prizes-7">[7]</a></sup>
</p><p>GIMPS also offers a US$3,000 research discovery award for participants who discover a new Mersenne prime of less than 100 million digits.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10">[10]</a></sup>
</p>
<h2><span class="mw-headline" id="History_of_largest_known_prime_numbers">History of largest known prime numbers</span><span class="mw-editsection">
<a role="button"
href="/w/index.php?title=Largest_known_prime_number&action=edit&section=3"title="Edit section: History of largest known prime numbers"
class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet ">
<span class="minerva-icon minerva-icon--edit"></span>
<span>edit</span>
</a>
</span>
</h2>
<figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:MersennePrimeStamp.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/0/05/MersennePrimeStamp.gif" decoding="async" width="287" height="94" class="mw-file-element" data-file-width="287" data-file-height="94" /></a><figcaption>Commemorative postmark used by the <a href="/wiki/University_of_Illinois_at_Urbana%E2%80%93Champaign" class="mw-redirect" title="University of Illinois at Urbana–Champaign">UIUC</a> Math Department after proving that M<sub>11213</sub> is prime</figcaption></figure>
<p>The following table lists the progression of the largest known prime number in ascending order.<sup id="cite_ref-computer_history_3-1" class="reference"><a href="#cite_note-computer_history-3">[3]</a></sup> Here <span class="nowrap">M<sub><i>p</i></sub> = 2<sup><i>p</i></sup> − 1</span> is the Mersenne number with exponent <i>p</i>, where <i>p</i> is a prime number. The longest record-holder known was <span class="nowrap">M<sub>19</sub> = 524,287</span>, which was the largest known prime for 144 years. No records are known prior to 1456.
</p>
<div style="clear:both;" class=""></div>
<table class="wikitable sortable" border="1">
<tbody><tr>
<th>Number
</th>
<th>Decimal expansion<br />(partial for numbers > M<sub>1000</sub>)
</th>
<th>Digits
</th>
<th>Year found
</th>
<th>Discoverer<br />
</th></tr>
<tr>
<td>M<sub>13</sub>
</td>
<td style="text-align:right;">8,191
</td>
<td style="text-align:right;">4
</td>
<td>1456
</td>
<td>Anonymous
</td></tr>
<tr>
<td>M<sub>17</sub>
</td>
<td style="text-align:right;">131,071
</td>
<td style="text-align:right;">6
</td>
<td>1588
</td>
<td><a href="/wiki/Pietro_Cataldi" title="Pietro Cataldi">Pietro Cataldi</a>
</td></tr>
<tr>
<td>M<sub>19</sub>
</td>
<td style="text-align:right;">524,287
</td>
<td style="text-align:right;">6
</td>
<td>1588
</td>
<td>Pietro Cataldi
</td></tr>
<tr>
<td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {2^{32}+1}{641}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mrow>
<msup>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<mn>32</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>641</mn>
</mfrac>
</mstyle>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\tfrac {2^{32}+1}{641}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c424efb9f41d70ad40e9e8685ce40cac849f1d5" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:5.258ex; height:4.176ex;" alt="{\displaystyle {\tfrac {2^{32}+1}{641}}}"></span>
</td>
<td style="text-align:right;">6,700,417
</td>
<td style="text-align:right;">7
</td>
<td>1732
</td>
<td><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a>?<br />Euler did not explicitly publish the primality of 6,700,417, but the techniques he had used to factorise 2<sup>32</sup> + 1 meant that he had already done most of the work needed to prove this, and some experts believe he knew of it.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11">[11]</a></sup>
</td></tr>
<tr>
<td>M<sub>31</sub>
</td>
<td style="text-align:right;"><a href="/wiki/2,147,483,647" title="2,147,483,647">2,147,483,647</a>
</td>
<td style="text-align:right;">10
</td>
<td>1772
</td>
<td>Leonhard Euler
</td></tr>
<tr>
<td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {10^{18}+1}{1000001}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mrow>
<msup>
<mn>10</mn>
<mrow class="MJX-TeXAtom-ORD">
<mn>18</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>1000001</mn>
</mfrac>
</mstyle>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\tfrac {10^{18}+1}{1000001}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2574683dd6a5453af3a02f471a2828e0f20f433" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:6.59ex; height:4.176ex;" alt="{\displaystyle {\tfrac {10^{18}+1}{1000001}}}"></span>
</td>
<td style="text-align:right;">999,999,000,001
</td>
<td style="text-align:right;">12
</td>
<td>1851
</td>
<td>Included (but question-marked) in a list of primes by Looff. Given his uncertainty, some do not include this as a record.
</td></tr>
<tr>
<td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {2^{64}+1}{274177}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mrow>
<msup>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<mn>64</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>274177</mn>
</mfrac>
</mstyle>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\tfrac {2^{64}+1}{274177}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88171e610d98a0dcf33be212e9a251b20c2b8be8" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:5.768ex; height:4.343ex;" alt="{\displaystyle {\tfrac {2^{64}+1}{274177}}}"></span>
</td>
<td style="text-align:right;">67,280,421,310,721
</td>
<td style="text-align:right;">14
</td>
<td>1855
</td>
<td><a href="/wiki/Thomas_Clausen_(mathematician)" title="Thomas Clausen (mathematician)">Thomas Clausen</a> (but no proof was provided).
</td></tr>
<tr>
<td>M<sub>127</sub>
</td>
<td style="text-align:right;">170,141,183,460,469,<wbr />231,731,687,303,715,<wbr />884,105,727
</td>
<td style="text-align:right;">39
</td>
<td>1876
</td>
<td><a href="/wiki/%C3%89douard_Lucas" title="Édouard Lucas">Édouard Lucas</a>
</td></tr>
<tr>
<td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\tfrac {2^{148}+1}{17}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mfrac>
<mrow>
<msup>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<mn>148</mn>
</mrow>
</msup>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mn>17</mn>
</mfrac>
</mstyle>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\tfrac {2^{148}+1}{17}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/088164f7c20021ddd1442b894c090940167d95ba" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:5.925ex; height:4.343ex;" alt="{\displaystyle {\tfrac {2^{148}+1}{17}}}"></span>
</td>
<td style="text-align:right;">20,988,936,657,440,<wbr />586,486,151,264,256,<wbr />610,222,593,863,921
</td>
<td style="text-align:right;">44
</td>
<td>1951
</td>
<td><a href="/w/index.php?title=Aim%C3%A9_Ferrier&action=edit&redlink=1" class="new" title="Aimé Ferrier (page does not exist)">Aimé Ferrier</a> with a mechanical calculator; the largest record not set by computer.
</td></tr>
<tr>
<td>180×(M<sub>127</sub>)<sup>2</sup>+1
</td>
<td>
<p>521064401567922879406069432539<wbr />095585333589848390805645835218<wbr />3851018372555735221
</p>
</td>
<td style="text-align:right;">79
</td>
<td>1951
</td>
<td><a href="/wiki/J._C._P._Miller" title="J. C. P. Miller">J. C. P. Miller</a> & <a href="/wiki/David_Wheeler_(computer_scientist)" title="David Wheeler (computer scientist)">D. J. Wheeler</a><sup id="cite_ref-12" class="reference"><a href="#cite_note-12">[12]</a></sup><br />Using <a href="/wiki/University_of_Cambridge_Mathematical_Laboratory" class="mw-redirect" title="University of Cambridge Mathematical Laboratory">Cambridge's</a> <a href="/wiki/Electronic_delay_storage_automatic_calculator" class="mw-redirect" title="Electronic delay storage automatic calculator">EDSAC</a> computer
</td></tr>
<tr>
<td>M<sub>521</sub>
</td>
<td>
<p>686479766013060971498190079908<wbr />139321726943530014330540939446<wbr />345918554318339765605212255964<wbr />066145455497729631139148085803<wbr />712198799971664381257402829111<wbr />5057151
</p>
</td>
<td style="text-align:right;">157
</td>
<td>1952
</td>
<td><a href="/wiki/Raphael_M._Robinson" title="Raphael M. Robinson">Raphael M. Robinson</a>
</td></tr>
<tr>
<td>M<sub>607</sub>
</td>
<td>
<p>531137992816767098689588206552<wbr />468627329593117727031923199444<wbr />138200403559860852242739162502<wbr />265229285668889329486246501015<wbr />346579337652707239409519978766<wbr />587351943831270835393219031728127
</p>
</td>
<td style="text-align:right;">183
</td>
<td>1952
</td>
<td>Raphael M. Robinson
</td></tr>
<tr>
<td>M<sub>1279</sub>
</td>
<td>104079321946...703168729087
</td>
<td style="text-align:right;">386
</td>
<td>1952
</td>
<td>Raphael M. Robinson
</td></tr>
<tr>
<td>M<sub>2203</sub>
</td>
<td>147597991521...686697771007
</td>
<td style="text-align:right;">664
</td>
<td>1952
</td>
<td>Raphael M. Robinson
</td></tr>
<tr>
<td>M<sub>2281</sub>
</td>
<td>446087557183...418132836351
</td>
<td style="text-align:right;">687
</td>
<td>1952
</td>
<td>Raphael M. Robinson
</td></tr>
<tr>
<td>M<sub>3217</sub>
</td>
<td>259117086013...362909315071
</td>
<td style="text-align:right;">969
</td>
<td>1957
</td>
<td><a href="/wiki/Hans_Riesel" title="Hans Riesel">Hans Riesel</a>
</td></tr>
<tr>
<td>M<sub>4423</sub>
</td>
<td>285542542228...902608580607
</td>
<td style="text-align:right;">1,332
</td>
<td>1961
</td>
<td><a href="/w/index.php?title=Alexander_Hurwitz&action=edit&redlink=1" class="new" title="Alexander Hurwitz (page does not exist)">Alexander Hurwitz</a>
</td></tr>
<tr>
<td>M<sub>9689</sub>
</td>
<td>478220278805...826225754111
</td>
<td style="text-align:right;">2,917
</td>
<td>1963
</td>
<td><a href="/wiki/Donald_B._Gillies" title="Donald B. Gillies">Donald B. Gillies</a>
</td></tr>
<tr>
<td>M<sub>9941</sub>
</td>
<td>346088282490...883789463551
</td>
<td style="text-align:right;">2,993
</td>
<td>1963
</td>
<td>Donald B. Gillies
</td></tr>
<tr>
<td>M<sub>11213</sub>
</td>
<td>281411201369...087696392191
</td>
<td style="text-align:right;">3,376
</td>
<td>1963
</td>
<td>Donald B. Gillies
</td></tr>
<tr>
<td>M<sub>19937</sub>
</td>
<td>431542479738...030968041471
</td>
<td style="text-align:right;">6,002
</td>
<td>1971
</td>
<td><a href="/wiki/Bryant_Tuckerman" title="Bryant Tuckerman">Bryant Tuckerman</a>
</td></tr>
<tr>
<td>M<sub>21701</sub>
</td>
<td>448679166119...353511882751
</td>
<td style="text-align:right;">6,533
</td>
<td>1978
</td>
<td>Laura A. Nickel and <a href="/wiki/Landon_Curt_Noll" title="Landon Curt Noll">Landon Curt Noll</a><sup id="cite_ref-isthe_13-0" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td>M<sub>23209</sub>
</td>
<td>402874115778...523779264511
</td>
<td style="text-align:right;">6,987
</td>
<td>1979
</td>
<td>Landon Curt Noll<sup id="cite_ref-isthe_13-1" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td>M<sub>44497</sub>
</td>
<td>854509824303...961011228671
</td>
<td style="text-align:right;">13,395
</td>
<td>1979
</td>
<td><a href="/wiki/David_Slowinski" title="David Slowinski">David Slowinski</a> and <a href="/wiki/Harry_L._Nelson" title="Harry L. Nelson">Harry L. Nelson</a><sup id="cite_ref-isthe_13-2" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td>M<sub>86243</sub>
</td>
<td>536927995502...709433438207
</td>
<td style="text-align:right;">25,962
</td>
<td>1982
</td>
<td>David Slowinski<sup id="cite_ref-isthe_13-3" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td>M<sub>132049</sub>
</td>
<td>512740276269...455730061311
</td>
<td style="text-align:right;">39,751
</td>
<td>1983
</td>
<td>David Slowinski<sup id="cite_ref-isthe_13-4" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td>M<sub>216091</sub>
</td>
<td>746093103064...103815528447
</td>
<td style="text-align:right;">65,050
</td>
<td>1985
</td>
<td>David Slowinski<sup id="cite_ref-isthe_13-5" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 391581\times 2^{216193}-1}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mn>391581</mn>
<mo>×<!-- × --></mo>
<msup>
<mn>2</mn>
<mrow class="MJX-TeXAtom-ORD">
<mn>216193</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle 391581\times 2^{216193}-1}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0c5dbc4532c26176361775212646229fd03f7d7" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:20.145ex; height:2.843ex;" alt="{\displaystyle 391581\times 2^{216193}-1}"></span>
</td>
<td>148140632376...836387377151
</td>
<td style="text-align:right;">65,087
</td>
<td>1989
</td>
<td>A group, "Amdahl Six": John Brown, <a href="/wiki/Landon_Curt_Noll" title="Landon Curt Noll">Landon Curt Noll</a>, B. K. Parady, Gene Ward Smith, Joel F. Smith, Sergio E. Zarantonello.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14">[14]</a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15">[15]</a></sup><br />Largest non-Mersenne prime that was the largest known prime when it was discovered.
</td></tr>
<tr>
<td>M<sub>756839</sub>
</td>
<td>174135906820...328544677887
</td>
<td style="text-align:right;">227,832
</td>
<td>1992
</td>
<td>David Slowinski and <a href="/wiki/Paul_Gage" class="mw-redirect" title="Paul Gage">Paul Gage</a><sup id="cite_ref-isthe_13-6" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td>M<sub>859433</sub>
</td>
<td>129498125604...243500142591
</td>
<td style="text-align:right;">258,716
</td>
<td>1994
</td>
<td>David Slowinski and Paul Gage<sup id="cite_ref-isthe_13-7" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td>M<sub>1257787</sub>
</td>
<td>412245773621...976089366527
</td>
<td style="text-align:right;">378,632
</td>
<td>1996
</td>
<td>David Slowinski and Paul Gage<sup id="cite_ref-isthe_13-8" class="reference"><a href="#cite_note-isthe-13">[13]</a></sup>
</td></tr>
<tr>
<td>M<sub>1398269</sub>
</td>
<td>814717564412...868451315711
</td>
<td style="text-align:right;">420,921
</td>
<td>1996
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Joel Armengaud
</td></tr>
<tr>
<td>M<sub>2976221</sub>
</td>
<td>623340076248...743729201151
</td>
<td style="text-align:right;">895,932
</td>
<td>1997
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Gordon Spence
</td></tr>
<tr>
<td>M<sub>3021377</sub>
</td>
<td>127411683030...973024694271
</td>
<td style="text-align:right;">909,526
</td>
<td>1998
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Roland Clarkson
</td></tr>
<tr>
<td>M<sub>6972593</sub>
</td>
<td>437075744127...142924193791
</td>
<td style="text-align:right;">2,098,960
</td>
<td>1999
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Nayan Hajratwala
</td></tr>
<tr>
<td>M<sub>13466917</sub>
</td>
<td>924947738006...470256259071
</td>
<td style="text-align:right;">4,053,946
</td>
<td>2001
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Michael Cameron
</td></tr>
<tr>
<td>M<sub>20996011</sub>
</td>
<td>125976895450...762855682047
</td>
<td style="text-align:right;">6,320,430
</td>
<td>2003
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Michael Shafer
</td></tr>
<tr>
<td>M<sub>24036583</sub>
</td>
<td>299410429404...882733969407
</td>
<td style="text-align:right;">7,235,733
</td>
<td>2004
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Josh Findley
</td></tr>
<tr>
<td>M<sub>25964951</sub>
</td>
<td>122164630061...280577077247
</td>
<td style="text-align:right;">7,816,230
</td>
<td>2005
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Martin Nowak
</td></tr>
<tr>
<td>M<sub>30402457</sub>
</td>
<td>315416475618...411652943871
</td>
<td style="text-align:right;">9,152,052
</td>
<td>2005
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, <a href="/wiki/University_of_Central_Missouri" title="University of Central Missouri">University of Central Missouri</a> professors <a href="/wiki/Curtis_Cooper_(mathematician)" title="Curtis Cooper (mathematician)">Curtis Cooper</a> and Steven Boone
</td></tr>
<tr>
<td>M<sub>32582657</sub>
</td>
<td>124575026015...154053967871
</td>
<td style="text-align:right;">9,808,358
</td>
<td>2006
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, <a href="/wiki/Curtis_Cooper_(mathematician)" title="Curtis Cooper (mathematician)">Curtis Cooper</a> and Steven Boone
</td></tr>
<tr>
<td>M<sub>43112609</sub>
</td>
<td>316470269330...166697152511
</td>
<td style="text-align:right;">12,978,189
</td>
<td>2008
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Edson Smith
</td></tr>
<tr>
<td>M<sub>57885161</sub>
</td>
<td>581887266232...071724285951
</td>
<td style="text-align:right;">17,425,170
</td>
<td>2013
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, <a href="/wiki/Curtis_Cooper_(mathematician)" title="Curtis Cooper (mathematician)">Curtis Cooper</a>
</td></tr>
<tr>
<td>M<sub>74207281</sub>
</td>
<td>300376418084...391086436351
</td>
<td style="text-align:right;">22,338,618
</td>
<td>2016
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, <a href="/wiki/Curtis_Cooper_(mathematician)" title="Curtis Cooper (mathematician)">Curtis Cooper</a>
</td></tr>
<tr>
<td>M<sub>77232917</sub>
</td>
<td>467333183359...069762179071
</td>
<td style="text-align:right;">23,249,425
</td>
<td>2017
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Jonathan Pace
</td></tr>
<tr>
<td>M<sub>82589933</sub>
</td>
<td>148894445742...325217902591
</td>
<td style="text-align:right;">24,862,048
</td>
<td>2018
</td>
<td><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a>, Patrick Laroche
</td></tr>
</tbody></table>
<p><a href="/wiki/GIMPS" class="mw-redirect" title="GIMPS">GIMPS</a> found the fifteen latest records (all of them Mersenne primes) on ordinary computers operated by participants around the world.
</p>
<h2><span class="mw-headline" id="The_twenty_largest_known_prime_numbers">The twenty largest known prime numbers</span><span class="mw-editsection">
<a role="button"
href="/w/index.php?title=Largest_known_prime_number&action=edit&section=4"title="Edit section: The twenty largest known prime numbers"
class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet ">
<span class="minerva-icon minerva-icon--edit"></span>
<span>edit</span>
</a>
</span>
</h2>
<p>A list of the 5,000 largest known primes is maintained by the <a href="/wiki/PrimePages" title="PrimePages">PrimePages</a>,<sup id="cite_ref-16" class="reference"><a href="#cite_note-16">[16]</a></sup> of which the twenty largest are listed below.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17">[17]</a></sup>
</p>
<table class="wikitable sortable">
<tbody><tr>
<th>Rank</th>
<th class="unsortable">Number</th>
<th>Discovered</th>
<th>Digits</th>
<th>Form</th>
<th class="unsortable">Ref
</th></tr>
<tr>
<td style="text-align:right;">1
</td>
<td>2<sup>82589933</sup> − 1
</td>
<td>2018-12-07
</td>
<td style="text-align:right;">24,862,048
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-GIMPS-2018_1-2" class="reference"><a href="#cite_note-GIMPS-2018-1">[1]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">2
</td>
<td>2<sup>77232917</sup> − 1
</td>
<td>2017-12-26
</td>
<td style="text-align:right;">23,249,425
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M77232917_18-0" class="reference"><a href="#cite_note-M77232917-18">[18]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">3
</td>
<td>2<sup>74207281</sup> − 1
</td>
<td>2016-01-07
</td>
<td style="text-align:right;">22,338,618
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M74207281_19-0" class="reference"><a href="#cite_note-M74207281-19">[19]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">4
</td>
<td>2<sup>57885161</sup> − 1
</td>
<td>2013-01-25
</td>
<td style="text-align:right;">17,425,170
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M57885161_20-0" class="reference"><a href="#cite_note-M57885161-20">[20]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">5
</td>
<td>2<sup><a href="/wiki/43,112,609_(number)" class="mw-redirect" title="43,112,609 (number)">43112609</a></sup> − 1
</td>
<td>2008-08-23
</td>
<td style="text-align:right;">12,978,189
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M43112609_21-0" class="reference"><a href="#cite_note-M43112609-21">[21]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">6
</td>
<td>2<sup>42643801</sup> − 1
</td>
<td>2009-06-04
</td>
<td style="text-align:right;">12,837,064
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M42643801_22-0" class="reference"><a href="#cite_note-M42643801-22">[22]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">7
</td>
<td><a href="/wiki/Cyclotomic_polynomial" title="Cyclotomic polynomial">Φ<sub>3</sub></a>(−516693<sup>1048576</sup>)
</td>
<td>2023-10-02
</td>
<td style="text-align:right;">11,981,518
</td>
<td><a href="/wiki/Unique_prime" class="mw-redirect" title="Unique prime">Generalized unique</a>
</td>
<td><sup id="cite_ref-23" class="reference"><a href="#cite_note-23">[23]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">8
</td>
<td>Φ<sub>3</sub>(−465859<sup>1048576</sup>)
</td>
<td>2023-05-31
</td>
<td style="text-align:right;">11,887,192
</td>
<td>Generalized unique
</td>
<td><sup id="cite_ref-24" class="reference"><a href="#cite_note-24">[24]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">9
</td>
<td>2<sup>37156667</sup> − 1
</td>
<td>2008-09-06
</td>
<td style="text-align:right;">11,185,272
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M43112609_21-1" class="reference"><a href="#cite_note-M43112609-21">[21]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">10
</td>
<td>2<sup>32582657</sup> − 1
</td>
<td>2006-09-04
</td>
<td style="text-align:right;">9,808,358
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M32582657_25-0" class="reference"><a href="#cite_note-M32582657-25">[25]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">11
</td>
<td>10223 × 2<sup>31172165</sup> + 1
</td>
<td>2016-10-31
</td>
<td style="text-align:right;">9,383,761
</td>
<td><a href="/wiki/Proth_prime" title="Proth prime">Proth</a>
</td>
<td><sup id="cite_ref-SOB31172165_26-0" class="reference"><a href="#cite_note-SOB31172165-26">[26]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">12
</td>
<td>2<sup>30402457</sup> − 1
</td>
<td>2005-12-15
</td>
<td style="text-align:right;">9,152,052
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M30402457_27-0" class="reference"><a href="#cite_note-M30402457-27">[27]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">13
</td>
<td>2<sup>25964951</sup> − 1
</td>
<td>2005-02-18
</td>
<td style="text-align:right;">7,816,230
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M25964951_28-0" class="reference"><a href="#cite_note-M25964951-28">[28]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">14
</td>
<td>2<sup>24036583</sup> − 1
</td>
<td>2004-05-15
</td>
<td style="text-align:right;">7,235,733
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M24036583_29-0" class="reference"><a href="#cite_note-M24036583-29">[29]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">15
</td>
<td>1963736<sup>1048576</sup> + 1
</td>
<td>2022-09-24
</td>
<td style="text-align:right;">6,598,776
</td>
<td><a href="/wiki/Fermat_number#Generalized_Fermat_numbers" title="Fermat number">Generalized Fermat</a>
</td>
<td><sup id="cite_ref-30" class="reference"><a href="#cite_note-30">[30]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">16
</td>
<td>1951734<sup>1048576</sup> + 1
</td>
<td>2022-08-09
</td>
<td style="text-align:right;">6,595,985
</td>
<td>Generalized Fermat
</td>
<td><sup id="cite_ref-31" class="reference"><a href="#cite_note-31">[31]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">17
</td>
<td>202705 × 2<sup>21320516</sup> + 1
</td>
<td>2021-12-01
</td>
<td style="text-align:right;">6,418,121
</td>
<td>Proth
</td>
<td><sup id="cite_ref-32" class="reference"><a href="#cite_note-32">[32]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">18
</td>
<td>2<sup>20996011</sup> − 1
</td>
<td>2003-11-17
</td>
<td style="text-align:right;">6,320,430
</td>
<td>Mersenne
</td>
<td><sup id="cite_ref-M20996011_33-0" class="reference"><a href="#cite_note-M20996011-33">[33]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">19
</td>
<td>1059094<sup>1048576</sup> + 1
</td>
<td>2018-10-31
</td>
<td style="text-align:right;">6,317,602
</td>
<td>Generalized Fermat
</td>
<td><sup id="cite_ref-34" class="reference"><a href="#cite_note-34">[34]</a></sup>
</td></tr>
<tr>
<td style="text-align:right;">20
</td>
<td>3 × 2<sup>20928756</sup> − 1
</td>
<td>2023-07-05
</td>
<td style="text-align:right;">6,300,184
</td>
<td><a href="/wiki/Thabit_number" title="Thabit number">Thabit</a>
</td>
<td><sup id="cite_ref-35" class="reference"><a href="#cite_note-35">[35]</a></sup>
</td></tr>
</tbody></table>
<h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection">
<a role="button"
href="/w/index.php?title=Largest_known_prime_number&action=edit&section=5"title="Edit section: See also"
class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet ">
<span class="minerva-icon minerva-icon--edit"></span>
<span>edit</span>
</a>
</span>
</h2>
<ul><li><a href="/wiki/List_of_largest_known_primes_and_probable_primes" title="List of largest known primes and probable primes">List of largest known primes and probable primes</a></li></ul>
<h2><span class="mw-headline" id="References">References</span><span class="mw-editsection">
<a role="button"
href="/w/index.php?title=Largest_known_prime_number&action=edit&section=6"title="Edit section: References"
class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet ">
<span class="minerva-icon minerva-icon--edit"></span>
<span>edit</span>
</a>
</span>
</h2>
<style data-mw-deduplicate="TemplateStyles:r1217336898">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist">
<div class="mw-references-wrap mw-references-columns"><ol class="references">
<li id="cite_note-GIMPS-2018-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-GIMPS-2018_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-GIMPS-2018_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-GIMPS-2018_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1215172403">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a{background-size:contain}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a{background-size:contain}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a{background-size:contain}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#2C882D;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911F}html.skin-theme-clientpref-night .mw-parser-output .cs1-visible-error,html.skin-theme-clientpref-night .mw-parser-output .cs1-hidden-error{color:#f8a397}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-visible-error,html.skin-theme-clientpref-os .mw-parser-output .cs1-hidden-error{color:#f8a397}html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911F}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/press/M82589933.html">"GIMPS Project Discovers Largest Known Prime Number: 2<sup>82,589,933</sup>-1"</a>. <i>Mersenne Research, Inc</i>. 21 December 2018<span class="reference-accessdate">. Retrieved <span class="nowrap">21 December</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Mersenne+Research%2C+Inc.&rft.atitle=GIMPS+Project+Discovers+Largest+Known+Prime+Number%3A+2%3Csup%3E82%2C589%2C933%3C%2Fsup%3E-1&rft.date=2018-12-21&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2Fpress%2FM82589933.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://t5k.org/primes/search.php?Number=100">"The largest known primes – Database Search Output"</a>. Prime Pages<span class="reference-accessdate">. Retrieved <span class="nowrap">19 March</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+largest+known+primes+%E2%80%93+Database+Search+Output&rft.pub=Prime+Pages&rft_id=https%3A%2F%2Ft5k.org%2Fprimes%2Fsearch.php%3FNumber%3D100&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-computer_history-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-computer_history_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-computer_history_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFCaldwell" class="citation web cs1">Caldwell, Chris. <a rel="nofollow" class="external text" href="http://t5k.org/notes/by_year.html">"The Largest Known Prime by Year: A Brief History"</a>. Prime Pages<span class="reference-accessdate">. Retrieved <span class="nowrap">19 March</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Largest+Known+Prime+by+Year%3A+A+Brief+History&rft.pub=Prime+Pages&rft.aulast=Caldwell&rft.aufirst=Chris&rft_id=http%3A%2F%2Ft5k.org%2Fnotes%2Fby_year.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">The last non-Mersenne to be the largest known prime, was <a rel="nofollow" class="external text" href="http://t5k.org/primes/page.php?id=390">391,581 ⋅ 2<sup>216,193</sup> − 1</a>; see also <a rel="nofollow" class="external text" href="http://t5k.org/notes/by_year.html">The Largest Known Prime by year: A Brief History</a> originally by Caldwell.</span>
</li>
<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.personal.psu.edu/sxt104/class/Math140H/PerfectNum.html">"Perfect Numbers"</a>. <i>Penn State University</i><span class="reference-accessdate">. Retrieved <span class="nowrap">6 October</span> 2019</span>. <q>An interesting side note is about the binary representations of those numbers...</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Penn+State+University&rft.atitle=Perfect+Numbers&rft_id=http%3A%2F%2Fwww.personal.psu.edu%2Fsxt104%2Fclass%2FMath140H%2FPerfectNum.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/press/M82589933.html">"51st Known Mersenne Prime Discovered"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=51st+Known+Mersenne+Prime+Discovered&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2Fpress%2FM82589933.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-prizes-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-prizes_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-prizes_7-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-prizes_7-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.eff.org/press/archives/2009/10/14-0">"Record 12-Million-Digit Prime Number Nets $100,000 Prize"</a>. <i>Electronic Frontier Foundation</i>. <a href="/wiki/Electronic_Frontier_Foundation" title="Electronic Frontier Foundation">Electronic Frontier Foundation</a>. October 14, 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">November 26,</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Electronic+Frontier+Foundation&rft.atitle=Record+12-Million-Digit+Prime+Number+Nets+%24100%2C000+Prize&rft.date=2009-10-14&rft_id=https%3A%2F%2Fwww.eff.org%2Fpress%2Farchives%2F2009%2F10%2F14-0&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Electronic Frontier Foundation, <a rel="nofollow" class="external text" href="https://www.eff.org/press/releases/big-prime-nets-big-prize">Big Prime Nets Big Prize</a>.</span>
</li>
<li id="cite_note-invention-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-invention_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20081102044641/http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html">"Best Inventions of 2008 - 29. The 46th Mersenne Prime"</a>. <i>Time</i>. <a href="/wiki/Time_Inc" class="mw-redirect" title="Time Inc">Time Inc</a>. October 29, 2008. Archived from <a rel="nofollow" class="external text" href="http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_1854157,00.html">the original</a> on November 2, 2008<span class="reference-accessdate">. Retrieved <span class="nowrap">January 17,</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Time&rft.atitle=Best+Inventions+of+2008+-+29.+The+46th+Mersenne+Prime&rft.date=2008-10-29&rft_id=http%3A%2F%2Fwww.time.com%2Ftime%2Fspecials%2Fpackages%2Farticle%2F0%2C28804%2C1852747_1854195_1854157%2C00.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/legal/">"GIMPS by Mersenne Research, Inc"</a>. <i>mersenne.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">21 November</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+by+Mersenne+Research%2C+Inc.&rft_id=https%3A%2F%2Fwww.mersenne.org%2Flegal%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite id="CITEREFEdward_Sandifer2014" class="citation book cs1">Edward Sandifer, C. (19 November 2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=3c6iBQAAQBAJ&pg=PA43"><i>How Euler Did Even More</i></a>. The Mathematical Association of America. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780883855843" title="Special:BookSources/9780883855843"><bdi>9780883855843</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+Euler+Did+Even+More&rft.pub=The+Mathematical+Association+of+America&rft.date=2014-11-19&rft.isbn=9780883855843&rft.aulast=Edward+Sandifer&rft.aufirst=C.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D3c6iBQAAQBAJ%26pg%3DPA43&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><a href="/wiki/J._C._P._Miller" title="J. C. P. Miller">J. Miller</a>, <a rel="nofollow" class="external text" href="https://doi.org/10.1038/168838b0">Large Prime Numbers</a>. <i>Nature</i> 168, 838 (1951).</span>
</li>
<li id="cite_note-isthe-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-isthe_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-isthe_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-isthe_13-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-isthe_13-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-isthe_13-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-isthe_13-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-isthe_13-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-isthe_13-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-isthe_13-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Landon_Curt_Noll" title="Landon Curt Noll">Landon Curt Noll</a>, <a rel="nofollow" class="external text" href="http://www.isthe.com/chongo/tech/math/prime/prime_press.html">Large Prime Number Found by SGI/Cray Supercomputer</a>.</span>
</li>
<li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2324686">Letters to the Editor</a>. <i>The American Mathematical Monthly</i> 97, no. 3 (1990), p. 214. Accessed May 22, 2020.</span>
</li>
<li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://t5k.org/bios/code.php?code=Z">Proof-code: Z</a>, The <a href="/wiki/Prime_Pages" class="mw-redirect" title="Prime Pages">Prime Pages</a>.</span>
</li>
<li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://t5k.org/primes/home.php">"The Prime Database: The List of Largest Known Primes Home Page"</a>. <i>t5k.org/primes</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 March</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=t5k.org%2Fprimes&rft.atitle=The+Prime+Database%3A+The+List+of+Largest+Known+Primes+Home+Page&rft_id=https%3A%2F%2Ft5k.org%2Fprimes%2Fhome.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://t5k.org/top20/page.php?id=3">"The Top Twenty: Largest Known Primes"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">19 March</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Top+Twenty%3A+Largest+Known+Primes&rft_id=https%3A%2F%2Ft5k.org%2Ftop20%2Fpage.php%3Fid%3D3&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M77232917-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-M77232917_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/press/M77232917.html">"GIMPS Project Discovers Largest Known Prime Number: 2<sup>77,232,917</sup>-1"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a><span class="reference-accessdate">. Retrieved <span class="nowrap">3 January</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Project+Discovers+Largest+Known+Prime+Number%3A+2%3Csup%3E77%2C232%2C917%3C%2Fsup%3E-1&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2Fpress%2FM77232917.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M74207281-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-M74207281_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M74207281">"GIMPS Project Discovers Largest Known Prime Number: 2<sup>74,207,281</sup>-1"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a><span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Project+Discovers+Largest+Known+Prime+Number%3A+2%3Csup%3E74%2C207%2C281%3C%2Fsup%3E-1&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM74207281&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M57885161-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-M57885161_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M57885161">"GIMPS Discovers 48th Mersenne Prime, 2<sup>57,885,161</sup>-1 is now the Largest Known Prime"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a>. 5 February 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Discovers+48th+Mersenne+Prime%2C+2%3Csup%3E57%2C885%2C161%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&rft.date=2013-02-05&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM57885161&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M43112609-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-M43112609_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-M43112609_21-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M43112609">"GIMPS Discovers 45th and 46th Mersenne Primes, 2<sup>43,112,609</sup>-1 is now the Largest Known Prime"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a>. 15 September 2008<span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Discovers+45th+and+46th+Mersenne+Primes%2C+2%3Csup%3E43%2C112%2C609%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&rft.date=2008-09-15&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM43112609&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M42643801-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-M42643801_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M42643801">"GIMPS Discovers 47th Mersenne Prime, 2<sup>42,643,801</sup>-1 is newest, but not the largest, known Mersenne Prime"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a>. 12 April 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Discovers+47th+Mersenne+Prime%2C+2%3Csup%3E42%2C643%2C801%3C%2Fsup%3E-1+is+newest%2C+but+not+the+largest%2C+known+Mersenne+Prime.&rft.date=2009-04-12&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM42643801&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://t5k.org/primes/page.php?id=136490">"PrimePage Primes: Phi(3, - 516693^1048576)"</a>. <i>t5k.org</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=t5k.org&rft.atitle=PrimePage+Primes%3A+Phi%283%2C+-+516693%5E1048576%29&rft_id=https%3A%2F%2Ft5k.org%2Fprimes%2Fpage.php%3Fid%3D136490&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://t5k.org/primes/page.php?id=136107">"PrimePage Primes: Phi(3, - 465859^1048576)"</a>. <i>t5k.org</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=t5k.org&rft.atitle=PrimePage+Primes%3A+Phi%283%2C+-+465859%5E1048576%29&rft_id=https%3A%2F%2Ft5k.org%2Fprimes%2Fpage.php%3Fid%3D136107&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M32582657-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-M32582657_25-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M32582657">"GIMPS Discovers 44th Mersenne Prime, 2<sup>32,582,657</sup>-1 is now the Largest Known Prime"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a>. 11 September 2006<span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Discovers+44th+Mersenne+Prime%2C+2%3Csup%3E32%2C582%2C657%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&rft.date=2006-09-11&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM32582657&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-SOB31172165-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-SOB31172165_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.primegrid.com/download/SOB-31172165.pdf">"PrimeGrid's Seventeen or Bust Subproject"</a> <span class="cs1-format">(PDF)</span>. <i>primegrid.com</i>. <a href="/wiki/PrimeGrid" title="PrimeGrid">PrimeGrid</a><span class="reference-accessdate">. Retrieved <span class="nowrap">30 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=primegrid.com&rft.atitle=PrimeGrid%27s+Seventeen+or+Bust+Subproject&rft_id=http%3A%2F%2Fwww.primegrid.com%2Fdownload%2FSOB-31172165.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M30402457-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-M30402457_27-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M30402457">"GIMPS Discovers 43rd Mersenne Prime, 2<sup>30,402,457</sup>-1 is now the Largest Known Prime"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a>. 24 December 2005<span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Discovers+43rd+Mersenne+Prime%2C+2%3Csup%3E30%2C402%2C457%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&rft.date=2005-12-24&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM30402457&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M25964951-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-M25964951_28-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M25964951">"GIMPS Discovers 42nd Mersenne Prime, 2<sup>25,964,951</sup>-1 is now the Largest Known Prime"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a>. 27 February 2005<span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Discovers+42nd+Mersenne+Prime%2C+2%3Csup%3E25%2C964%2C951%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&rft.date=2005-02-27&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM25964951&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M24036583-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-M24036583_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M24036583">"GIMPS Discovers 41st Mersenne Prime, 2<sup>24,036,583</sup>-1 is now the Largest Known Prime"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a>. 28 May 2004<span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Discovers+41st+Mersenne+Prime%2C+2%3Csup%3E24%2C036%2C583%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&rft.date=2004-05-28&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM24036583&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.primegrid.com/download/GFN-1963736_1048576.pdf">"PrimeGrid's Generalized Fermat Prime Search"</a> <span class="cs1-format">(PDF)</span>. <i>primegrid.com</i>. <a href="/wiki/PrimeGrid" title="PrimeGrid">PrimeGrid</a><span class="reference-accessdate">. Retrieved <span class="nowrap">7 October</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=primegrid.com&rft.atitle=PrimeGrid%27s+Generalized+Fermat+Prime+Search&rft_id=https%3A%2F%2Fwww.primegrid.com%2Fdownload%2FGFN-1963736_1048576.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.primegrid.com/download/GFN-1951734_1048576.pdf">"PrimeGrid's Generalized Fermat Prime Search"</a> <span class="cs1-format">(PDF)</span>. <i>primegrid.com</i>. <a href="/wiki/PrimeGrid" title="PrimeGrid">PrimeGrid</a><span class="reference-accessdate">. Retrieved <span class="nowrap">17 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=primegrid.com&rft.atitle=PrimeGrid%27s+Generalized+Fermat+Prime+Search&rft_id=https%3A%2F%2Fwww.primegrid.com%2Fdownload%2FGFN-1951734_1048576.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.primegrid.com/download/ESP-202705.pdf">"PrimeGrid's Extended Sierpinski Problem Prime Search"</a> <span class="cs1-format">(PDF)</span>. <i>primegrid.com</i>. <a href="/wiki/PrimeGrid" title="PrimeGrid">PrimeGrid</a><span class="reference-accessdate">. Retrieved <span class="nowrap">28 December</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=primegrid.com&rft.atitle=PrimeGrid%27s+Extended+Sierpinski+Problem+Prime+Search&rft_id=http%3A%2F%2Fwww.primegrid.com%2Fdownload%2FESP-202705.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-M20996011-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-M20996011_33-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M20996011">"GIMPS Discovers 40th Mersenne Prime, 2<sup>20,996,011</sup>-1 is now the Largest Known Prime"</a>. <i>mersenne.org</i>. <a href="/wiki/Great_Internet_Mersenne_Prime_Search" title="Great Internet Mersenne Prime Search">Great Internet Mersenne Prime Search</a>. 2 December 2003<span class="reference-accessdate">. Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=mersenne.org&rft.atitle=GIMPS+Discovers+40th+Mersenne+Prime%2C+2%3Csup%3E20%2C996%2C011%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&rft.date=2003-12-02&rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM20996011&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.primegrid.com/download/GFN-1059094_1048576.pdf">"PrimeGrid's Generalized Fermat Prime Search"</a> <span class="cs1-format">(PDF)</span>. <i>primegrid.com</i>. <a href="/wiki/PrimeGrid" title="PrimeGrid">PrimeGrid</a><span class="reference-accessdate">. Retrieved <span class="nowrap">7 November</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=primegrid.com&rft.atitle=PrimeGrid%27s+Generalized+Fermat+Prime+Search&rft_id=https%3A%2F%2Fwww.primegrid.com%2Fdownload%2FGFN-1059094_1048576.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
<li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1215172403"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.primegrid.com/download/321-20928756.pdf">"PrimeGrid's 321 Prime Search"</a> <span class="cs1-format">(PDF)</span>. <i>primegrid.com</i>. <a href="/wiki/PrimeGrid" title="PrimeGrid">PrimeGrid</a><span class="reference-accessdate">. Retrieved <span class="nowrap">17 July</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=primegrid.com&rft.atitle=PrimeGrid%27s+321+Prime+Search&rft_id=https%3A%2F%2Fwww.primegrid.com%2Fdownload%2F321-20928756.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALargest+known+prime+number" class="Z3988"></span></span>
</li>
</ol></div></div>
<h2><span class="mw-headline" id="External_links">External links</span><span class="mw-editsection">
<a role="button"
href="/w/index.php?title=Largest_known_prime_number&action=edit&section=7"title="Edit section: External links"
class="cdx-button cdx-button--size-large cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--icon-only cdx-button--weight-quiet ">
<span class="minerva-icon minerva-icon--edit"></span>
<span>edit</span>
</a>
</span>
</h2>
<ul><li><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M82589933">Press release about the largest known prime 2<sup>82,589,933</sup>−1</a></li>
<li><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M77232917">Press release about the former largest known prime 2<sup>77,232,917</sup>−1</a></li>
<li><a rel="nofollow" class="external text" href="https://www.mersenne.org/primes/?press=M74207281">Press release about the former largest known prime 2<sup>74,207,281</sup>−1</a></li></ul>
<div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1061467846">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style></div><div role="navigation" class="navbox" aria-labelledby="Prime_number_classes" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1063604349">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Prime_number_classes" title="Template:Prime number classes"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Prime_number_classes" title="Template talk:Prime number classes"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Prime_number_classes" title="Special:EditPage/Template:Prime number classes"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Prime_number_classes" style="font-size:114%;margin:0 4em"><a href="/wiki/Prime_number" title="Prime number">Prime number</a> classes</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">By formula</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Fermat_number" title="Fermat number">Fermat (<span class="texhtml texhtml-big" style="font-size:110%;">2<sup>2<sup><i>n</i></sup></sup> + 1</span>)</a></li>
<li><a href="/wiki/Mersenne_prime" title="Mersenne prime">Mersenne (<span class="texhtml texhtml-big" style="font-size:110%;">2<sup><i>p</i></sup> − 1</span>)</a></li>
<li><a href="/wiki/Double_Mersenne_number" title="Double Mersenne number">Double Mersenne (<span class="texhtml texhtml-big" style="font-size:110%;">2<sup>2<sup><i>p</i></sup>−1</sup> − 1</span>)</a></li>
<li><a href="/wiki/Wagstaff_prime" title="Wagstaff prime">Wagstaff <span class="texhtml texhtml-big" style="font-size:110%;">(2<sup><i>p</i></sup> + 1)/3</span></a></li>
<li><a href="/wiki/Proth_prime" title="Proth prime">Proth (<span class="texhtml texhtml-big" style="font-size:110%;"><i>k</i>·2<sup><i>n</i></sup> + 1</span>)</a></li>
<li><a href="/wiki/Factorial_prime" title="Factorial prime">Factorial (<span class="texhtml texhtml-big" style="font-size:110%;"><i>n</i>! ± 1</span>)</a></li>
<li><a href="/wiki/Primorial_prime" title="Primorial prime">Primorial (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p<sub>n</sub></i># ± 1</span>)</a></li>
<li><a href="/wiki/Euclid_number" title="Euclid number">Euclid (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p<sub>n</sub></i># + 1</span>)</a></li>
<li><a href="/wiki/Pythagorean_prime" title="Pythagorean prime">Pythagorean (<span class="texhtml texhtml-big" style="font-size:110%;">4<i>n</i> + 1</span>)</a></li>
<li><a href="/wiki/Pierpont_prime" title="Pierpont prime">Pierpont (<span class="texhtml texhtml-big" style="font-size:110%;">2<sup><i>m</i></sup>·3<sup><i>n</i></sup> + 1</span>)</a></li>
<li><a href="/wiki/Quartan_prime" title="Quartan prime">Quartan (<span class="texhtml texhtml-big" style="font-size:110%;"><i>x</i><sup>4</sup> + <i>y</i><sup>4</sup></span>)</a></li>
<li><a href="/wiki/Solinas_prime" title="Solinas prime">Solinas (<span class="texhtml texhtml-big" style="font-size:110%;">2<sup><i>m</i></sup> ± 2<sup><i>n</i></sup> ± 1</span>)</a></li>
<li><a href="/wiki/Cullen_number" title="Cullen number">Cullen (<span class="texhtml texhtml-big" style="font-size:110%;"><i>n</i>·2<sup><i>n</i></sup> + 1</span>)</a></li>
<li><a href="/wiki/Woodall_number" title="Woodall number">Woodall (<span class="texhtml texhtml-big" style="font-size:110%;"><i>n</i>·2<sup><i>n</i></sup> − 1</span>)</a></li>
<li><a href="/wiki/Cuban_prime" title="Cuban prime">Cuban (<span class="texhtml texhtml-big" style="font-size:110%;"><i>x</i><sup>3</sup> − <i>y</i><sup>3</sup>)/(<i>x</i> − <i>y</i></span>)</a></li>
<li><a href="/wiki/Leyland_number" title="Leyland number">Leyland (<span class="texhtml texhtml-big" style="font-size:110%;"><i>x<sup>y</sup></i> + <i>y<sup>x</sup></i></span>)</a></li>
<li><a href="/wiki/Thabit_number" title="Thabit number">Thabit (<span class="texhtml texhtml-big" style="font-size:110%;">3·2<sup><i>n</i></sup> − 1</span>)</a></li>
<li><a href="/wiki/Williams_number" title="Williams number">Williams (<span class="texhtml texhtml-big" style="font-size:110%;">(<i>b</i>−1)·<i>b</i><sup><i>n</i></sup> − 1</span>)</a></li>
<li><a href="/wiki/Mills%27_constant" title="Mills' constant">Mills (<span class="texhtml texhtml-big" style="font-size:110%;"><span style="font-size:1em">⌊</span><i>A</i><sup>3<sup><i>n</i></sup></sup><span style="font-size:1em">⌋</span></span>)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By integer sequence</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Fibonacci_prime" title="Fibonacci prime">Fibonacci</a></li>
<li><a href="/wiki/Lucas_prime" class="mw-redirect" title="Lucas prime">Lucas</a></li>
<li><a href="/wiki/Pell_prime" class="mw-redirect" title="Pell prime">Pell</a></li>
<li><a href="/wiki/Newman%E2%80%93Shanks%E2%80%93Williams_prime" title="Newman–Shanks–Williams prime">Newman–Shanks–Williams</a></li>
<li><a href="/wiki/Perrin_prime" class="mw-redirect" title="Perrin prime">Perrin</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By property</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Wieferich_prime" title="Wieferich prime">Wieferich</a> (<a href="/wiki/Wieferich_pair" title="Wieferich pair">pair</a>)</li>
<li><a href="/wiki/Wall%E2%80%93Sun%E2%80%93Sun_prime" title="Wall–Sun–Sun prime">Wall–Sun–Sun</a></li>
<li><a href="/wiki/Wolstenholme_prime" title="Wolstenholme prime">Wolstenholme</a></li>
<li><a href="/wiki/Wilson_prime" title="Wilson prime">Wilson</a></li>
<li><a href="/wiki/Lucky_number" title="Lucky number">Lucky</a></li>
<li><a href="/wiki/Fortunate_number" title="Fortunate number">Fortunate</a></li>
<li><a href="/wiki/Ramanujan_prime" title="Ramanujan prime">Ramanujan</a></li>
<li><a href="/wiki/Pillai_prime" title="Pillai prime">Pillai</a></li>
<li><a href="/wiki/Regular_prime" title="Regular prime">Regular</a></li>
<li><a href="/wiki/Strong_prime" title="Strong prime">Strong</a></li>
<li><a href="/wiki/Stern_prime" title="Stern prime">Stern</a></li>
<li><a href="/wiki/Supersingular_prime_(algebraic_number_theory)" title="Supersingular prime (algebraic number theory)">Supersingular (elliptic curve)</a></li>
<li><a href="/wiki/Supersingular_prime_(moonshine_theory)" title="Supersingular prime (moonshine theory)">Supersingular (moonshine theory)</a></li>
<li><a href="/wiki/Good_prime" title="Good prime">Good</a></li>
<li><a href="/wiki/Super-prime" title="Super-prime">Super</a></li>
<li><a href="/wiki/Higgs_prime" title="Higgs prime">Higgs</a></li>
<li><a href="/wiki/Highly_cototient_number" title="Highly cototient number">Highly cototient</a></li>
<li><a href="/wiki/Reciprocals_of_primes#Unique_primes" title="Reciprocals of primes">Unique</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Radix" title="Radix">Base</a>-dependent</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Palindromic_prime" title="Palindromic prime">Palindromic</a></li>
<li><a href="/wiki/Emirp" title="Emirp">Emirp</a></li>
<li><a href="/wiki/Repunit" title="Repunit">Repunit <span class="texhtml texhtml-big" style="font-size:110%;">(10<sup><i>n</i></sup> − 1)/9</span></a></li>
<li><a href="/wiki/Permutable_prime" title="Permutable prime">Permutable</a></li>
<li><a href="/wiki/Circular_prime" title="Circular prime">Circular</a></li>
<li><a href="/wiki/Truncatable_prime" title="Truncatable prime">Truncatable</a></li>
<li><a href="/wiki/Minimal_prime_(recreational_mathematics)" title="Minimal prime (recreational mathematics)">Minimal</a></li>
<li><a href="/wiki/Delicate_prime" title="Delicate prime">Delicate</a></li>
<li><a href="/wiki/Primeval_number" title="Primeval number">Primeval</a></li>
<li><a href="/wiki/Full_reptend_prime" title="Full reptend prime">Full reptend</a></li>
<li><a href="/wiki/Unique_prime_number" class="mw-redirect" title="Unique prime number">Unique</a></li>
<li><a href="/wiki/Happy_number#Happy_primes" title="Happy number">Happy</a></li>
<li><a href="/wiki/Self_number" title="Self number">Self</a></li>
<li><a href="/wiki/Smarandache%E2%80%93Wellin_prime" class="mw-redirect" title="Smarandache–Wellin prime">Smarandache–Wellin</a></li>
<li><a href="/wiki/Strobogrammatic_prime" class="mw-redirect" title="Strobogrammatic prime">Strobogrammatic</a></li>
<li><a href="/wiki/Dihedral_prime" title="Dihedral prime">Dihedral</a></li>
<li><a href="/wiki/Tetradic_number" title="Tetradic number">Tetradic</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Patterns</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Twin_prime" title="Twin prime">Twin (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p</i>, <i>p</i> + 2</span>)</a></li>
<li><a href="/wiki/Bi-twin_chain" title="Bi-twin chain">Bi-twin chain (<span class="texhtml texhtml-big" style="font-size:110%;"><i>n</i> ± 1, 2<i>n</i> ± 1, 4<i>n</i> ± 1, …</span>)</a></li>
<li><a href="/wiki/Prime_triplet" title="Prime triplet">Triplet (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p</i>, <i>p</i> + 2 or <i>p</i> + 4, <i>p</i> + 6</span>)</a></li>
<li><a href="/wiki/Prime_quadruplet" title="Prime quadruplet">Quadruplet (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p</i>, <i>p</i> + 2, <i>p</i> + 6, <i>p</i> + 8</span>)</a></li>
<li><a href="/wiki/Prime_k-tuple" title="Prime k-tuple"><i>k</i>-tuple</a></li>
<li><a href="/wiki/Cousin_prime" title="Cousin prime">Cousin (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p</i>, <i>p</i> + 4</span>)</a></li>
<li><a href="/wiki/Sexy_prime" title="Sexy prime">Sexy (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p</i>, <i>p</i> + 6</span>)</a></li>
<li><a href="/wiki/Chen_prime" title="Chen prime">Chen</a></li>
<li><a href="/wiki/Safe_and_Sophie_Germain_primes" title="Safe and Sophie Germain primes">Sophie Germain/Safe (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p</i>, 2<i>p</i> + 1</span>)</a></li>
<li><a href="/wiki/Cunningham_chain" title="Cunningham chain">Cunningham (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p</i>, 2<i>p</i> ± 1, 4<i>p</i> ± 3, 8<i>p</i> ± 7, ...</span>)</a></li>
<li><a href="/wiki/Primes_in_arithmetic_progression" title="Primes in arithmetic progression">Arithmetic progression (<span class="texhtml texhtml-big" style="font-size:110%;"><i>p</i> + <i>a·n</i>, <i>n</i> = 0, 1, 2, 3, ...</span>)</a></li>
<li><a href="/wiki/Balanced_prime" title="Balanced prime">Balanced (<span class="texhtml texhtml-big" style="font-size:110%;">consecutive <i>p</i> − <i>n</i>, <i>p</i>, <i>p</i> + <i>n</i></span>)</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">By size</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Megaprime" title="Megaprime">Mega (1,000,000+ digits)</a></li>
<li><a class="mw-selflink selflink">Largest known</a>
<ul><li><a href="/wiki/List_of_largest_known_primes_and_probable_primes" title="List of largest known primes and probable primes">list</a></li></ul></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Complex_number" title="Complex number">Complex numbers</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Eisenstein_prime" class="mw-redirect" title="Eisenstein prime">Eisenstein prime</a></li>
<li><a href="/wiki/Gaussian_integer#Gaussian_primes" title="Gaussian integer">Gaussian prime</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Composite_number" title="Composite number">Composite numbers</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Pseudoprime" title="Pseudoprime">Pseudoprime</a>
<ul><li><a href="/wiki/Catalan_pseudoprime" title="Catalan pseudoprime">Catalan</a></li>
<li><a href="/wiki/Elliptic_pseudoprime" title="Elliptic pseudoprime">Elliptic</a></li>
<li><a href="/wiki/Euler_pseudoprime" title="Euler pseudoprime">Euler</a></li>
<li><a href="/wiki/Euler%E2%80%93Jacobi_pseudoprime" title="Euler–Jacobi pseudoprime">Euler–Jacobi</a></li>
<li><a href="/wiki/Fermat_pseudoprime" title="Fermat pseudoprime">Fermat</a></li>
<li><a href="/wiki/Frobenius_pseudoprime" title="Frobenius pseudoprime">Frobenius</a></li>
<li><a href="/wiki/Lucas_pseudoprime" title="Lucas pseudoprime">Lucas</a></li>
<li><a href="/wiki/Perrin_pseudoprime" class="mw-redirect" title="Perrin pseudoprime">Perrin</a></li>
<li><a href="/wiki/Somer%E2%80%93Lucas_pseudoprime" title="Somer–Lucas pseudoprime">Somer–Lucas</a></li>
<li><a href="/wiki/Strong_pseudoprime" title="Strong pseudoprime">Strong</a></li></ul></li>
<li><a href="/wiki/Carmichael_number" title="Carmichael number">Carmichael number</a></li>
<li><a href="/wiki/Almost_prime" title="Almost prime">Almost prime</a></li>
<li><a href="/wiki/Semiprime" title="Semiprime">Semiprime</a></li>
<li><a href="/wiki/Sphenic_number" title="Sphenic number">Sphenic number</a></li>
<li><a href="/wiki/Interprime" title="Interprime">Interprime</a></li>
<li><a href="/wiki/Pernicious_number" title="Pernicious number">Pernicious</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Probable_prime" title="Probable prime">Probable prime</a></li>
<li><a href="/wiki/Industrial-grade_prime" title="Industrial-grade prime">Industrial-grade prime</a></li>
<li><a href="/wiki/Illegal_prime" class="mw-redirect" title="Illegal prime">Illegal prime</a></li>
<li><a href="/wiki/Formula_for_primes" title="Formula for primes">Formula for primes</a></li>
<li><a href="/wiki/Prime_gap" title="Prime gap">Prime gap</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">First 60 primes</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/2" title="2">2</a></li>
<li><a href="/wiki/3" title="3">3</a></li>
<li><a href="/wiki/5" title="5">5</a></li>
<li><a href="/wiki/7" title="7">7</a></li>
<li><a href="/wiki/11_(number)" title="11 (number)">11</a></li>
<li><a href="/wiki/13_(number)" title="13 (number)">13</a></li>
<li><a href="/wiki/17_(number)" title="17 (number)">17</a></li>
<li><a href="/wiki/19_(number)" title="19 (number)">19</a></li>
<li><a href="/wiki/23_(number)" title="23 (number)">23</a></li>
<li><a href="/wiki/29_(number)" title="29 (number)">29</a></li>
<li><a href="/wiki/31_(number)" title="31 (number)">31</a></li>
<li><a href="/wiki/37_(number)" title="37 (number)">37</a></li>
<li><a href="/wiki/41_(number)" title="41 (number)">41</a></li>
<li><a href="/wiki/43_(number)" title="43 (number)">43</a></li>
<li><a href="/wiki/47_(number)" title="47 (number)">47</a></li>
<li><a href="/wiki/53_(number)" title="53 (number)">53</a></li>
<li><a href="/wiki/59_(number)" title="59 (number)">59</a></li>
<li><a href="/wiki/61_(number)" title="61 (number)">61</a></li>
<li><a href="/wiki/67_(number)" title="67 (number)">67</a></li>
<li><a href="/wiki/71_(number)" title="71 (number)">71</a></li>
<li><a href="/wiki/73_(number)" title="73 (number)">73</a></li>
<li><a href="/wiki/79_(number)" title="79 (number)">79</a></li>
<li><a href="/wiki/83_(number)" title="83 (number)">83</a></li>
<li><a href="/wiki/89_(number)" title="89 (number)">89</a></li>
<li><a href="/wiki/97_(number)" title="97 (number)">97</a></li>
<li><a href="/wiki/101_(number)" title="101 (number)">101</a></li>
<li><a href="/wiki/103_(number)" title="103 (number)">103</a></li>
<li><a href="/wiki/107_(number)" title="107 (number)">107</a></li>
<li><a href="/wiki/109_(number)" title="109 (number)">109</a></li>
<li><a href="/wiki/113_(number)" title="113 (number)">113</a></li>
<li><a href="/wiki/127_(number)" title="127 (number)">127</a></li>
<li><a href="/wiki/131_(number)" title="131 (number)">131</a></li>
<li><a href="/wiki/137_(number)" title="137 (number)">137</a></li>
<li><a href="/wiki/139_(number)" title="139 (number)">139</a></li>
<li><a href="/wiki/149_(number)" title="149 (number)">149</a></li>
<li><a href="/wiki/151_(number)" title="151 (number)">151</a></li>
<li><a href="/wiki/157_(number)" title="157 (number)">157</a></li>
<li><a href="/wiki/163_(number)" title="163 (number)">163</a></li>
<li><a href="/wiki/167_(number)" title="167 (number)">167</a></li>
<li><a href="/wiki/173_(number)" title="173 (number)">173</a></li>
<li><a href="/wiki/179_(number)" title="179 (number)">179</a></li>
<li><a href="/wiki/181_(number)" title="181 (number)">181</a></li>
<li><a href="/wiki/191_(number)" title="191 (number)">191</a></li>
<li><a href="/wiki/193_(number)" title="193 (number)">193</a></li>
<li><a href="/wiki/197_(number)" title="197 (number)">197</a></li>
<li><a href="/wiki/199_(number)" title="199 (number)">199</a></li>
<li><a href="/wiki/211_(number)" title="211 (number)">211</a></li>
<li><a href="/wiki/223_(number)" title="223 (number)">223</a></li>
<li><a href="/wiki/227_(number)" title="227 (number)">227</a></li>
<li><a href="/wiki/229_(number)" title="229 (number)">229</a></li>
<li><a href="/wiki/233_(number)" title="233 (number)">233</a></li>
<li><a href="/wiki/239_(number)" title="239 (number)">239</a></li>
<li><a href="/wiki/241_(number)" title="241 (number)">241</a></li>
<li><a href="/wiki/251_(number)" title="251 (number)">251</a></li>
<li><a href="/wiki/257_(number)" title="257 (number)">257</a></li>
<li><a href="/wiki/263_(number)" title="263 (number)">263</a></li>
<li><a href="/wiki/269_(number)" title="269 (number)">269</a></li>
<li><a href="/wiki/271_(number)" title="271 (number)">271</a></li>
<li><a href="/wiki/277_(number)" title="277 (number)">277</a></li>
<li><a href="/wiki/281_(number)" title="281 (number)">281</a></li></ul>
</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="2"><div><a href="/wiki/List_of_prime_numbers" title="List of prime numbers">List of prime numbers</a></div></td></tr></tbody></table></div>
<div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1061467846"></div><div role="navigation" class="navbox" aria-labelledby="Large_numbers" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1063604349"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Large_numbers" title="Template:Large numbers"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Large_numbers" title="Template talk:Large numbers"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Large_numbers" title="Special:EditPage/Template:Large numbers"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Large_numbers" style="font-size:114%;margin:0 4em"><a href="/wiki/Large_numbers" title="Large numbers">Large numbers</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Examples <br />in<br />numerical <br />order</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/1000_(number)" title="1000 (number)">Thousand</a></li>
<li><a href="/wiki/10,000" title="10,000">Ten thousand</a></li>
<li><a href="/wiki/100,000" title="100,000">Hundred thousand</a></li>
<li><a href="/wiki/1,000,000" title="1,000,000">Million</a></li>
<li><a href="/wiki/10,000,000" title="10,000,000">Ten million</a></li>
<li><a href="/wiki/100,000,000" title="100,000,000">Hundred million</a></li>
<li><a href="/wiki/1,000,000,000" title="1,000,000,000">Billion</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)#1012" title="Orders of magnitude (numbers)">Trillion</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)#1015" title="Orders of magnitude (numbers)">Quadrillion</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)#1018" title="Orders of magnitude (numbers)">Quintillion</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)#1021" title="Orders of magnitude (numbers)">Sextillion</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)#1024" title="Orders of magnitude (numbers)">Septillion</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)#1027" title="Orders of magnitude (numbers)">Octillion</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)#1030" title="Orders of magnitude (numbers)">Nonillion</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)#1033" title="Orders of magnitude (numbers)">Decillion</a></li>
<li><a href="/wiki/Eddington_number" title="Eddington number">Eddington number</a></li>
<li><a href="/wiki/Googol" title="Googol">Googol</a></li>
<li><a href="/wiki/Shannon_number" title="Shannon number">Shannon number</a></li>
<li><a href="/wiki/Googolplex" title="Googolplex">Googolplex</a></li>
<li><a href="/wiki/Skewes%27s_number" title="Skewes's number">Skewes's number</a></li>
<li><a href="/wiki/Steinhaus%E2%80%93Moser_notation" title="Steinhaus–Moser notation">Moser's number</a></li>
<li><a href="/wiki/Graham%27s_number" title="Graham's number">Graham's number</a></li>
<li><a href="/wiki/Kruskal%27s_tree_theorem" title="Kruskal's tree theorem">TREE(3)</a></li>
<li><a href="/wiki/Friedman%27s_SSCG_function" title="Friedman's SSCG function">SSCG(3)</a></li>
<li><a href="/wiki/Buchholz_hydra#BH(n)" title="Buchholz hydra">BH(3)</a></li>
<li><a href="/wiki/Rayo%27s_number" title="Rayo's number">Rayo's number</a></li>
<li><a href="/wiki/Transfinite_number" title="Transfinite number">Transfinite numbers</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Expression<br />methods</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Notations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Scientific_notation" title="Scientific notation">Scientific notation</a></li>
<li><a href="/wiki/Knuth%27s_up-arrow_notation" title="Knuth's up-arrow notation">Knuth's up-arrow notation</a></li>
<li><a href="/wiki/Conway_chained_arrow_notation" title="Conway chained arrow notation">Conway chained arrow notation</a></li>
<li><a href="/wiki/Steinhaus%E2%80%93Moser_notation" title="Steinhaus–Moser notation">Steinhaus–Moser notation</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Operators</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Hyperoperation" title="Hyperoperation">Hyperoperation</a>
<ul><li><a href="/wiki/Tetration" title="Tetration">Tetration</a></li>
<li><a href="/wiki/Pentation" title="Pentation">Pentation</a></li></ul></li>
<li><a href="/wiki/Ackermann_function" title="Ackermann function">Ackermann function</a></li>
<li><a href="/wiki/Grzegorczyk_hierarchy" title="Grzegorczyk hierarchy">Grzegorczyk hierarchy</a></li>
<li><a href="/wiki/Fast-growing_hierarchy" title="Fast-growing hierarchy">Fast-growing hierarchy</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related <br />articles<br />(alphabetical <br />order)<br /></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">
<ul><li><a href="/wiki/Busy_beaver" title="Busy beaver">Busy beaver</a></li>
<li><a href="/wiki/Extended_real_number_line" title="Extended real number line">Extended real number line</a></li>
<li><a href="/wiki/Indefinite_and_fictitious_numbers" title="Indefinite and fictitious numbers">Indefinite and fictitious numbers</a></li>
<li><a href="/wiki/Infinitesimal" title="Infinitesimal">Infinitesimal</a></li>
<li><a class="mw-selflink selflink">Largest known prime number</a></li>
<li><a href="/wiki/List_of_numbers" title="List of numbers">List of numbers</a></li>
<li><a href="/wiki/Long_and_short_scales" title="Long and short scales">Long and short scales</a></li>
<li><a href="/wiki/Number" title="Number">Number systems</a></li>
<li><a href="/wiki/Numeral_(linguistics)" title="Numeral (linguistics)">Number names</a></li>
<li><a href="/wiki/Orders_of_magnitude_(numbers)" title="Orders of magnitude (numbers)">Orders of magnitude</a></li>
<li><a href="/wiki/Power_of_two" title="Power of two">Power of two</a></li>
<li><a href="/wiki/Power_of_three" title="Power of three">Power of three</a></li>
<li><a href="/wiki/Power_of_10" title="Power of 10">Power of 10</a></li>
<li><a href="/wiki/Carl_Sagan#Sagan_units" title="Carl Sagan">Sagan Unit</a></li></ul>
</div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="font-weight:bold;"><div>
<ul><li><a href="/wiki/Names_of_large_numbers" title="Names of large numbers">Names</a></li>
<li><a href="/wiki/History_of_large_numbers" title="History of large numbers">History</a></li></ul>
</div></td></tr></tbody></table></div></div>' |
Whether or not the change was made through a Tor exit node (tor_exit_node ) | false |
Unix timestamp of change (timestamp ) | '1713689096' |