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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]].]]
[[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]].]]

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'{{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&nbsp;''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&nbsp;''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]]'
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'@@ -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]].]] '
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[ 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>' ]
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[ 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>' ]
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'<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">&#91;1&#93;</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&#39;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&#160;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&amp;action=edit">&#91;update&#93;</a></sup>, the six largest known primes are Mersenne primes.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">&#91;2&#93;</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">&#91;3&#93;</a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4">&#91;4&#93;</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">&#91;5&#93;</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&amp;action=edit&amp;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">&#91;1&#93;</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">&#91;6&#93;</a></sup> </p> </blockquote> <p>As of February&#160;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&amp;action=edit">&#91;update&#93;</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&amp;action=edit&amp;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">&#91;7&#93;</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">&#91;8&#93;</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">&#91;7&#93;</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">&#91;9&#93;</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">&#91;7&#93;</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">&#91;10&#93;</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&amp;action=edit&amp;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">&#91;3&#93;</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&#160;<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 &gt; 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">&#91;11&#93;</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&amp;action=edit&amp;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> &amp; <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">&#91;12&#93;</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&amp;action=edit&amp;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">&#91;13&#93;</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">&#91;13&#93;</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">&#91;13&#93;</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">&#91;13&#93;</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">&#91;13&#93;</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">&#91;13&#93;</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>&#x00D7;<!-- × --></mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>216193</mn> </mrow> </msup> <mo>&#x2212;<!-- − --></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">&#91;14&#93;</a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15">&#91;15&#93;</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">&#91;13&#93;</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">&#91;13&#93;</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">&#91;13&#93;</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&amp;action=edit&amp;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">&#91;16&#93;</a></sup> of which the twenty largest are listed below.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17">&#91;17&#93;</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">&#91;1&#93;</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">&#91;18&#93;</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">&#91;19&#93;</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">&#91;20&#93;</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">&#91;21&#93;</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">&#91;22&#93;</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">&#91;23&#93;</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">&#91;24&#93;</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">&#91;21&#93;</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">&#91;25&#93;</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">&#91;26&#93;</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">&#91;27&#93;</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">&#91;28&#93;</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">&#91;29&#93;</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">&#91;30&#93;</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">&#91;31&#93;</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">&#91;32&#93;</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">&#91;33&#93;</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">&#91;34&#93;</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">&#91;35&#93;</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&amp;action=edit&amp;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&amp;action=edit&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=Mersenne+Research%2C+Inc.&amp;rft.atitle=GIMPS+Project+Discovers+Largest+Known+Prime+Number%3A+2%3Csup%3E82%2C589%2C933%3C%2Fsup%3E-1&amp;rft.date=2018-12-21&amp;rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2Fpress%2FM82589933.html&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=The+largest+known+primes+%E2%80%93+Database+Search+Output&amp;rft.pub=Prime+Pages&amp;rft_id=https%3A%2F%2Ft5k.org%2Fprimes%2Fsearch.php%3FNumber%3D100&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=The+Largest+Known+Prime+by+Year%3A+A+Brief+History&amp;rft.pub=Prime+Pages&amp;rft.aulast=Caldwell&amp;rft.aufirst=Chris&amp;rft_id=http%3A%2F%2Ft5k.org%2Fnotes%2Fby_year.html&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=Penn+State+University&amp;rft.atitle=Perfect+Numbers&amp;rft_id=http%3A%2F%2Fwww.personal.psu.edu%2Fsxt104%2Fclass%2FMath140H%2FPerfectNum.html&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=51st+Known+Mersenne+Prime+Discovered&amp;rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2Fpress%2FM82589933.html&amp;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">. 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Retrieved <span class="nowrap">29 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=mersenne.org&amp;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.&amp;rft.date=2009-04-12&amp;rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM42643801&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=t5k.org&amp;rft.atitle=PrimePage+Primes%3A+Phi%283%2C+-+516693%5E1048576%29&amp;rft_id=https%3A%2F%2Ft5k.org%2Fprimes%2Fpage.php%3Fid%3D136490&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=t5k.org&amp;rft.atitle=PrimePage+Primes%3A+Phi%283%2C+-+465859%5E1048576%29&amp;rft_id=https%3A%2F%2Ft5k.org%2Fprimes%2Fpage.php%3Fid%3D136107&amp;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">. 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Retrieved <span class="nowrap">30 September</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=primegrid.com&amp;rft.atitle=PrimeGrid%27s+Seventeen+or+Bust+Subproject&amp;rft_id=http%3A%2F%2Fwww.primegrid.com%2Fdownload%2FSOB-31172165.pdf&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=mersenne.org&amp;rft.atitle=GIMPS+Discovers+43rd+Mersenne+Prime%2C+2%3Csup%3E30%2C402%2C457%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&amp;rft.date=2005-12-24&amp;rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM30402457&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=mersenne.org&amp;rft.atitle=GIMPS+Discovers+42nd+Mersenne+Prime%2C+2%3Csup%3E25%2C964%2C951%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&amp;rft.date=2005-02-27&amp;rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM25964951&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=mersenne.org&amp;rft.atitle=GIMPS+Discovers+41st+Mersenne+Prime%2C+2%3Csup%3E24%2C036%2C583%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&amp;rft.date=2004-05-28&amp;rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM24036583&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=primegrid.com&amp;rft.atitle=PrimeGrid%27s+Generalized+Fermat+Prime+Search&amp;rft_id=https%3A%2F%2Fwww.primegrid.com%2Fdownload%2FGFN-1963736_1048576.pdf&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=primegrid.com&amp;rft.atitle=PrimeGrid%27s+Generalized+Fermat+Prime+Search&amp;rft_id=https%3A%2F%2Fwww.primegrid.com%2Fdownload%2FGFN-1951734_1048576.pdf&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=primegrid.com&amp;rft.atitle=PrimeGrid%27s+Extended+Sierpinski+Problem+Prime+Search&amp;rft_id=http%3A%2F%2Fwww.primegrid.com%2Fdownload%2FESP-202705.pdf&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=mersenne.org&amp;rft.atitle=GIMPS+Discovers+40th+Mersenne+Prime%2C+2%3Csup%3E20%2C996%2C011%3C%2Fsup%3E-1+is+now+the+Largest+Known+Prime.&amp;rft.date=2003-12-02&amp;rft_id=https%3A%2F%2Fwww.mersenne.org%2Fprimes%2F%3Fpress%3DM20996011&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=primegrid.com&amp;rft.atitle=PrimeGrid%27s+Generalized+Fermat+Prime+Search&amp;rft_id=https%3A%2F%2Fwww.primegrid.com%2Fdownload%2FGFN-1059094_1048576.pdf&amp;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&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=primegrid.com&amp;rft.atitle=PrimeGrid%27s+321+Prime+Search&amp;rft_id=https%3A%2F%2Fwww.primegrid.com%2Fdownload%2F321-20928756.pdf&amp;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&amp;action=edit&amp;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 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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>&#160;+&#160;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>&#160;−&#160;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>&#160;−&#160;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>&#160;+&#160;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>&#160;+&#160;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>!&#160;±&#160;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>#&#160;±&#160;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>#&#160;+&#160;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>&#160;+&#160;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>&#160;+&#160;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>&#160;+&#160;<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>&#160;±&#160;2<sup><i>n</i></sup>&#160;±&#160;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>&#160;+&#160;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>&#160;−&#160;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>&#160;−&#160;<i>y</i><sup>3</sup>)/(<i>x</i>&#160;−&#160;<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>&#160;+&#160;<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>&#160;−&#160;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>&#160;−&#160;1</span>)</a></li> <li><a href="/wiki/Mills%27_constant" title="Mills&#39; 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>&#160;−&#160;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>&#160;+&#160;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>&#160;±&#160;1, 2<i>n</i>&#160;±&#160;1, 4<i>n</i>&#160;±&#160;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>&#160;+&#160;2 or <i>p</i>&#160;+&#160;4, <i>p</i>&#160;+&#160;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>&#160;+&#160;2, <i>p</i>&#160;+&#160;6, <i>p</i>&#160;+&#160;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>&#160;+&#160;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>&#160;+&#160;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>&#160;+&#160;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>&#160;±&#160;1, 4<i>p</i>&#160;±&#160;3, 8<i>p</i>&#160;±&#160;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>&#160;+&#160;<i>a·n</i>, <i>n</i>&#160;=&#160;0,&#160;1,&#160;2,&#160;3,&#160;...</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>&#160;−&#160;<i>n</i>, <i>p</i>, <i>p</i>&#160;+&#160;<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&#39;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&#39;s number">Graham's number</a></li> <li><a href="/wiki/Kruskal%27s_tree_theorem" title="Kruskal&#39;s tree theorem">TREE(3)</a></li> <li><a href="/wiki/Friedman%27s_SSCG_function" title="Friedman&#39;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&#39;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&#39;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'