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* ''M''<sub>''n''</sub> denotes the Mersenne prime <math>2^n{-}1</math>
+
{{Last update|2019-02-19}}
−
* ''P''<sub>''n''</sub> denotes the Perfect number <math>2^{n-1}\cdot(2^n{-}1)</math>
+
==Explanations==
−
 
+
*'''#''': number count of the Mersenne primes linked to that prime page
−
{| cellpadding="4" border="1" style="margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
+
*'''n-value''': value of exponent and if available link to [[The Prime Pages]] entry
−
|- bgcolor="lightblue"
+
*'''Digits in M<sub>n</sub>''': denotes the [[Mersenne prime]] 2<sup>n</sup>-1 and a downloadable decimal representation
−
! #
+
*'''Digits in P<sub>n</sub>''': denotes the [[Perfect number]] 2<sup>n-1</sup> &bull; (2<sup>n</sup>-1) and a downloadable decimal representation
−
! ''n''
+
*'''Value of M<sub>n</sub>''': the first/last digits of the Mersenne number (or whole for smaller ones)
−
! Digits in ''M''<sub>''n''</sub>
+
*'''Date''': year/date of discovery, if available a link to the press release by [[GIMPS]]
−
! Digits in ''P''<sub>''n''</sub>
+
*'''Discoverer & Credits''': listed the discoverer(s) and credited [[person]]/[[project]]
−
! Value of ''M''<sub>''n''</sub>
 
−
! Date of<br>discovery
 
−
! Discoverer
 
−
|-
 
−
| align="right" | [[M1|1]]
 
−
| align="right" | 2
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M2.txt 1]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect2.txt 1]
 
−
| align="right" | 3
 
−
| align="right" | c. 430 BCE
 
−
| align="right" | Ancient Greek mathematicians
 
−
|-
 
−
| align="right" | [[M2|2]]
 
−
| align="right" | 3
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M3.txt 1]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect3.txt 2]
 
−
| align="right" | 7
 
−
| align="right" | c. 430 BCE
 
−
| align="right" | Ancient Greek mathematicians
 
−
|-
 
−
| align="right" | [[M3|3]]
 
−
| align="right" | 5
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M5.txt 2]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect5.txt 3]
 
−
| align="right" | 31
 
−
| align="right" | c. 300 BCE
 
−
| align="right" | Ancient Greek mathematicians
 
−
|-
 
−
| align="right" | [[M4|4]]
 
−
| align="right" | 7
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M7.txt 3]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect7.txt 4]
 
−
| align="right" | 127
 
−
| align="right" | c. 300 BCE
 
−
| align="right" | Ancient Greek mathematicians
 
−
|-
 
−
| align="right" | [[M5|5]]
 
−
| align="right" | 13
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M13.txt 4]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect13.txt 8]
 
−
| align="right" | 8191
 
−
| align="right" | 1456
 
−
| align="right" | ''anonymous''
 
−
|-
 
−
| align="right" | [[M6|6]]
 
−
| align="right" | 17
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M17.txt 6]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect17.txt 10]
 
−
| align="right" | 131071
 
−
| align="right" | 1588
 
−
| align="right" | Cataldi
 
−
|-
 
−
| align="right" | [[M7|7]]
 
−
| align="right" | 19
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M19.txt 6]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect19.txt 12]
 
−
| align="right" | 524287
 
−
| align="right" | 1588
 
−
| align="right" | Cataldi
 
−
|-
 
−
| align="right" | [[M8|8]]
 
−
| align="right" | 31
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M31.txt 10]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect31.txt 19]
 
−
| align="right" | 2147483647
 
−
| align="right" | 1772
 
−
| align="right" | [[Leonhard Euler]]
 
−
|-
 
−
| align="right" | [[M9|9]]
 
−
| align="right" | 61
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M61.txt 19]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect61.txt 37]
 
−
| align="right" | 2305843009213693951
 
−
| align="right" | 1883
 
−
| align="right" | [[Ivan Mikheevich Pervushin]]
 
−
|-
 
−
| align="right" | [[M10|10]]
 
−
| align="right" | 89
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M89.txt 27]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect89.txt 54]
 
−
| align="right" | 618970019642...137449562111
 
−
| align="right" | 1911
 
−
| align="right" | Powers
 
−
|-
 
−
| align="right" | [[M11|11]]
 
−
| align="right" | 107
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M107.txt 33]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect107.txt 65]
 
−
| align="right" | 162259276829...578010288127
 
−
| align="right" | 1914
 
−
| align="right" | Powers
 
−
|-
 
−
| align="right" | [[M12|12]]
 
−
| align="right" | 127
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M127.txt 39]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect127.txt 77]
 
−
| align="right" | 170141183460...715884105727
 
−
| align="right" | 1876
 
−
| align="right" | [[Edouard Lucas]]
 
−
|-
 
−
| align="right" | [[M13|13]]
 
−
| align="right" | 521
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M521.txt 157]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect521.txt 314]
 
−
| align="right" | 686479766013...291115057151
 
−
| align="right" | 1952-01-30
 
−
| align="right" | [[Raphael Robinson]]
 
−
|-
 
−
| align="right" | [[M14|14]]
 
−
| align="right" | 607
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M607.txt 183]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect607.txt 366]
 
−
| align="right" | 531137992816...219031728127
 
−
| align="right" | 1952-01-30
 
−
| align="right" | [[Raphael Robinson]]
 
−
|-
 
−
| align="right" | [[M15|15]]
 
−
| align="right" | 1,279
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M1279.txt 386]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect1279.txt 770]
 
−
| align="right" | 104079321946...703168729087
 
−
| align="right" | 1952-06-25
 
−
| align="right" | [[Raphael Robinson]]
 
−
|-
 
−
| align="right" | [[M16|16]]
 
−
| align="right" | 2,203
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M2203.txt 664]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect2203.txt 1,327]
 
−
| align="right" | 147597991521...686697771007
 
−
| align="right" | 1952-10-07
 
−
| align="right" | [[Raphael Robinson]]
 
−
|-
 
−
| align="right" | [[M17|17]]
 
−
| align="right" | 2,281
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M2281.txt 687]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect2281.txt 1,373]
 
−
| align="right" | 446087557183...418132836351
 
−
| align="right" | 1952-11-09
 
−
| align="right" | [[Raphael Robinson]]
 
−
|-
 
−
| align="right" | [[M18|18]]
 
−
| align="right" | 3,217
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M3217.txt 969]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect3217.txt 1,937]
 
−
| align="right" | 259117086013...362909315071
 
−
| align="right" | 1957-09-08
 
−
| align="right" | [[Hans Riesel]]
 
−
|-
 
−
| align="right" | [[M19|19]]
 
−
| align="right" | 4,253
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M4253.txt 1,281]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect4253.txt 2,561]
 
−
| align="right" | 190797007524...815350484991
 
−
| align="right" | 1961-11-03
 
−
| align="right" | Hurwitz
 
−
|-
 
−
| align="right" | [[M20|20]]
 
−
| align="right" | 4,423
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M4423.txt 1,332]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect4423.txt 2,663]
 
−
| align="right" | 285542542228...902608580607
 
−
| align="right" | 1961-11-03
 
−
| align="right" | Hurwitz
 
−
|-
 
−
| align="right" | [[M21|21]]
 
−
| align="right" | 9,689
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M9689.txt 2,917]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect9689.txt 5,834]
 
−
| align="right" | 478220278805...826225754111
 
−
| align="right" | 1963-05-11
 
−
| align="right" | Gillies
 
−
|-
 
−
| align="right" | [[M22|22]]
 
−
| align="right" | 9,941
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M9941.txt 2,993]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect9941.txt 5,985]
 
−
| align="right" | 346088282490...883789463551
 
−
| align="right" | 1963-05-16
 
−
| align="right" | Gillies
 
−
|-
 
−
| align="right" | [[M23|23]]
 
−
| align="right" | 11,213
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M11213.txt 3,376]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect11213.txt 6,751]
 
−
| align="right" | 281411201369...087696392191
 
−
| align="right" | 1963-06-02
 
−
| align="right" | Gillies
 
−
|-
 
−
| align="right" | [[M24|24]]
 
−
| align="right" | 19,937
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M19937.txt 6,002]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect19937.txt 12,003]
 
−
| align="right" | 431542479738...030968041471
 
−
| align="right" | 1971-03-04
 
−
| align="right" | Tuckerman
 
−
|-
 
−
| align="right" | [[M25|25]]
 
−
| align="right" | 21,701
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M21701.txt 6,533]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect21701.txt 13,066]
 
−
| align="right" | 448679166119...353511882751
 
−
| align="right" | 1978-10-30
 
−
| align="right" | [[Landon Curt Noll]] &amp; [[Laura A. Nickel]]
 
−
|-
 
−
| align="right" | [[M26|26]]
 
−
| align="right" | 23,209
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M23209.txt 6,987]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect23209.txt 13,973]
 
−
| align="right" | 402874115778...523779264511
 
−
| align="right" | 1979-02-09
 
−
| align="right" | [[Landon Curt Noll]]
 
−
|-
 
−
| align="right" | [[M27|27]]
 
−
| align="right" | 44,497
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M44497.txt 13,395]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect44497.txt 26,790]
 
−
| align="right" | 854509824303...961011228671
 
−
| align="right" | 1979-04-08
 
−
| align="right" | Nelson &amp; [[David Slowinski]]
 
−
|-
 
−
| align="right" | [[M28|28]]
 
−
| align="right" | 86,243
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M86243.txt 25,962]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect86243.txt 51,924]
 
−
| align="right" | 536927995502...709433438207
 
−
| align="right" | 1982-09-25
 
−
| align="right" | [[David Slowinski]]
 
−
|-
 
−
| align="right" | [[M29|29]]
 
−
| align="right" | 110,503
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M110503.txt 33,265]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect110503.txt 66,530]
 
−
| align="right" | 521928313341...083465515007
 
−
| align="right" | 1988-01-28
 
−
| align="right" | Colquitt &amp; Welsh
 
−
|-
 
−
| align="right" | [[M30|30]]
 
−
| align="right" | 132,049
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M132049.txt 39,751]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect132049.txt 79,502]
 
−
| align="right" | 512740276269...455730061311
 
−
| align="right" | 1983-09-20
 
−
| align="right" | [[David Slowinski]]
 
−
|-
 
−
| align="right" | [[M31|31]]
 
−
| align="right" | 216,091
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M216091.txt 65,050]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect216091.txt 130,100]
 
−
| align="right" | 746093103064...103815528447
 
−
| align="right" | 1985-09-06
 
−
| align="right" | [[David Slowinski]]
 
−
|-
 
−
| align="right" | [[M32|32]]
 
−
| align="right" | 756,839
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M756839.zip 227,832]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect756839.zip 455,663]
 
−
| align="right" | 174135906820...328544677887
 
−
| align="right" | 1992-02-19
 
−
| align="right" | [[David Slowinski]], [[Paul Gage]] &amp; [[Harwell]]
 
−
|-
 
−
| align="right" | [[M33|33]]
 
−
| align="right" | 859,433
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M859433.zip 258,716]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect859433.zip 517,430]
 
−
| align="right" | 129498125604...243500142591
 
−
| align="right" | 1994-01-10
 
−
| align="right" | [[David Slowinski]] &amp; [[Paul Gage]]
 
−
|-
 
−
| align="right" | [[M34|34]]
 
−
| align="right" | 1,257,787
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M1257787.zip 378,632]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect1257787.zip 757,263]
 
−
| align="right" | 412245773621...976089366527
 
−
| align="right" | 1996-09-03
 
−
| align="right" | [[David Slowinski]] &amp; [[Paul Gage]]
 
−
|-
 
−
| align="right" | [[M35|35]]
 
−
| align="right" | 1,398,269
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M1398269.zip 420,921]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect1398269.zip 841,842]
 
−
| align="right" | 814717564412...868451315711
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M1398269 1996-11-13]
 
−
| align="right" | [[Joel Armengaud]], [[George Woltman]] et. al. [[GIMPS]]
 
−
|-
 
−
| align="right" | [[M36|36]]
 
−
| align="right" | 2,976,221
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M2976221.zip 895,932]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect2976221.zip 1,791,864]
 
−
| align="right" | 623340076248...743729201151
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M2976221 1997-08-24]
 
−
| align="right" | [[Gordon Spence]], [[George Woltman]] et. al. [[GIMPS]]
 
−
|-
 
−
| align="right" | [[M37|37]]
 
−
| align="right" | 3,021,377
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M3021377.zip 909,526]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect3021377.zip 1,819,050]
 
−
| align="right" | 127411683030...973024694271
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M3021377 1998-01-27]
 
−
| align="right" | [[Roland Clarkson]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M38|38]]
 
−
| align="right" | 6,972,593
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M6972593.zip 2,098,960]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect6972593.zip 4,197,919]
 
−
| align="right" | 437075744127...142924193791
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M6972593 1999-06-01]
 
−
| align="right" | [[Nayan Hajratwala]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M39|39]]
 
−
| align="right" | 13,466,917
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M13466917.zip 4,053,946]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect13466917.zip 8,107,892]
 
−
| align="right" | 924947738006...470256259071
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M13466917 2001-11-14]
 
−
| align="right" | [[Michael Cameron]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M40|40]]
 
−
| align="right" | 20,996,011
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M20996011.zip 6,320,430]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect20996011.zip 12,640,858]
 
−
| align="right" | 125976895450...762855682047
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M20996011 2003-11-17]
 
−
| align="right" | [[Michael Shafer]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M41|41]]
 
−
| align="right" | 24,036,583
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M24036583.zip 7,235,733]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect24036583.zip 14,471,465]
 
−
| align="right" | 299410429404...882733969407
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M24036583 2004-05-15]
 
−
| align="right" | [[Josh Findley]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M42|42]]
 
−
| align="right" | 25,964,951
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M25964951.zip 7,816,230]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect25964951.zip 15,632,458]
 
−
| align="right" | 122164630061...280577077247
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M25964951 2005-02-18]
 
−
| align="right" | [[Martin Nowak]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M43|43]]
 
−
| align="right" | 30,402,457
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M30402457.zip 9,152,052]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect30402457.zip 18,304,103]
 
−
| align="right" | 315416475618...411652943871
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M30402457 2005-12-15]
 
−
| align="right" | [[Curtis Cooper]], [[Steven Boone]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M44|44]]
 
−
| align="right" | 32,582,657
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M32582657.zip 9,808,358]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect32582657.zip 19,616,714]
 
−
| align="right" | 124575026015...154053967871
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M32582657 2006-09-04]
 
−
| align="right" | [[Curtis Cooper]], [[Steven Boone]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M45|45]]
 
−
| align="right" | 37,156,667
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M37156667.zip 11,185,272]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect37156667.zip 22,370,543]
 
−
| align="right" | 202254406890...022308220927
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M37156667 2008-09-06]
 
−
| align="right" | [[Hans-Michael Elvenich]], [[George Woltman]], [[Scott Kurowski]], et al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M46|46]]
 
−
| align="right" | 42,643,801
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M42643801.zip 12,837,064]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect42643801.zip 25,674,127]
 
−
| align="right" | 169873516452...765562314751
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M42643801 2009-04-12]
 
−
| align="right" | [[Odd Magnar Strindmo|Odd M. Strindmo]], [[George Woltman]], [[Scott Kurowski]], et al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M47|47]]
 
−
| align="right" | 43,112,609
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M43112609.zip 12,978,189]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect43112609.zip 25,957,378]
 
−
| align="right" | 316470269330...166697152511
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M43112609 2008-08-23]
 
−
| align="right" | [[Edson Smith]], [[George Woltman]], [[Scott Kurowski]], et al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M48|48]]<sup>*</sup>
 
−
| align="right" | 57,885,161
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M57885161.zip 17,425,170]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect57885161.zip 34,850,340]
 
−
| align="right" | 581887266232...071724285951
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M57885161 2013-01-25]
 
−
| align="right" | [[Curtis Cooper]], [[George Woltman]], [[Scott Kurowski]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M49|49]]<sup>*</sup>
 
−
| align="right" | 74,207,281
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M74207281.zip 22,338,618]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect74207281.zip 44,677,236]
 
−
| align="right" | 300376418084...391086436351
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M74207281 2016-01-07]
 
−
| align="right" | [[Curtis Cooper]], [[George Woltman]], [[Scott Kurowski]], [[Aaron Blosser]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M50|50]]<sup>*</sup>
 
−
| align="right" | 77,232,917
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M77232917.zip 23,249,425]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect77232917.zip 46,498,850]
 
−
| align="right" | 467333183359...069762179071
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M77232917 2017-12-26]
 
−
| align="right" | [[Jonathan Pace]], [[George Woltman]], [[Scott Kurowski]], [[Aaron Blosser]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|-
 
−
| align="right" | [[M51|51]]<sup>*</sup>
 
−
| align="right" | 82,589,933
 
−
| align="right" | [https://www.mersenne.org/primes/digits/M82589933.zip 24,862,048]
 
−
| align="right" | [https://www.mersenne.org/primes/perfect/perfect82589933.zip 49,724,095]
 
−
| align="right" | 148894445742...325217902591
 
−
| align="right" | [https://www.mersenne.org/primes/?press=M82589933 2018-12-07]
 
−
| align="right" | [[Patrick Laroche]], [[George Woltman]], [[Aaron Blosser]] et. al. [[GIMPS]] &amp; [[PrimeNet]]
 
−
|}
 
−
 
 
−
<sup>*</sup>It is not known whether any undiscovered Mersenne primes exist
 
−
between the 48th (M<sub>57 885 161</sub>) and the 51th (M<sub>82 589 933</sub>) on this chart; the ranking is therefore provisional.
 
  
 +
==Data table==
 
{{#dpl:
 
{{#dpl:
−
|category=Category:Mersenne prime
+
|category=Category:Mersenne prime
−
|nottitlematch=Mersenne prime
+
|nottitlematch=Mersenne prime
−
|order=ascending
+
|order=ascending
−
|ordermethod=sortkey
+
|ordermethod=sortkey
−
|include={InfoboxMersennePrime}:title:nvalue:digits:pdigits:number:discovery:discoverer
+
|include={InfoboxMersennePrime} dpl
−
|table=class="wikitable sortable",-,#,n,Digits<br>in M<sub>n</sub>,Digits<br>in P<sub>n</sub>,Value<br>of M<sub>n</sub>,Date,Discoverer
+
|table=class="wikitable sortable",-,#,n-value,Digits in ''M<sub>n</sub>'',Digits in ''P<sub>n</sub>'',Value of ''M<sub>n</sub>'',Date,Discoverer & Credits
−
|tablerow=align=right{{!}}[[%%]],align=right{{!}}%%,align=right{{!}}%%,align=right{{!}}%%,align=center{{!}}%%,align=left{{!}}%%
+
|tablerow=%%
 
}}
 
}}
 +
:{{C|red|'''*'''}} = Provisional ranking
  
 
==See also==
 
==See also==
Line 447: Line 34:
 
*[http://www.utm.edu/research/primes/mersenne/LukeMirror/biblio.htm Mersenne Prime Bibliography] with Hyperlinks to original publications
 
*[http://www.utm.edu/research/primes/mersenne/LukeMirror/biblio.htm Mersenne Prime Bibliography] with Hyperlinks to original publications
 
*[http://www.taz.de/pt/2005/03/11/a0355.nf/text dpa - reportage about prime mersenne number] - detection in detail (German)
 
*[http://www.taz.de/pt/2005/03/11/a0355.nf/text dpa - reportage about prime mersenne number] - detection in detail (German)
−
*[[Wikipedia:Mersenne_prime|Wikipedia]]
+
*[[Wikipedia:Mersenne_prime|Mersenne prime]]
 
[[Category:Mersenne prime]]
 
[[Category:Mersenne prime]]

Latest revision as of 09:44, 6 March 2019

Last update: 2019-02-19

Explanations

  • #: number count of the Mersenne primes linked to that prime page
  • n-value: value of exponent and if available link to The Prime Pages entry
  • Digits in Mn: denotes the Mersenne prime 2n-1 and a downloadable decimal representation
  • Digits in Pn: denotes the Perfect number 2n-1 • (2n-1) and a downloadable decimal representation
  • Value of Mn: the first/last digits of the Mersenne number (or whole for smaller ones)
  • Date: year/date of discovery, if available a link to the press release by GIMPS
  • Discoverer & Credits: listed the discoverer(s) and credited person/project

Data table

# n-value Digits in Mn Digits in Pn Value of Mn Date Discoverer & Credits
M1 2 1 1 3 c. 430 BCE Ancient Greek mathematicians
M2 3 1 2 7 c. 430 BCE Ancient Greek mathematicians
M3 5 2 3 31 c. 300 BCE Ancient Greek mathematicians
M4 7 3 4 127 c. 300 BCE Ancient Greek mathematicians
M5 13 4 8 8191 1456 anonymous
M6 17 6 10 131071 1588 Pietro Cataldi
M7 19 6 12 524287 1588 Pietro Cataldi
M8 31 10 19 2147483647 1772 Leonhard Euler
M9 61 19 37 2305843009213693951 1883 Ivan Mikheevich Pervushin
M10 89 27 54 618970019642...137449562111 1911 Ralph Ernest Powers‏‎
M11 107 33 65 162259276829...578010288127 1914-06-11 Ralph Ernest Powers‏‎
M12 127 39 77 170141183460...715884105727 1876-01-10 Édouard Lucas
M13 521 157 314 686479766013...291115057151 1952-01-30 Raphael M. Robinson
M14 607 183 366 531137992816...219031728127 1952-01-30 Raphael M. Robinson
M15 1,279 386 770 104079321946...703168729087 1952-06-25 Raphael M. Robinson
M16 2,203 664 1,327 147597991521...686697771007 1952-10-07 Raphael M. Robinson
M17 2,281 687 1,373 446087557183...418132836351 1952-10-09 Raphael M. Robinson
M18 3,217 969 1,937 259117086013...362909315071 1957-09-08 Hans Riesel
M19 4,253 1,281 2,561 190797007524...815350484991 1961-11-03 Alexander Hurwitz
M20 4,423 1,332 2,663 285542542228...902608580607 1961-11-03 Alexander Hurwitz
M21 9,689 2,917 5,834 478220278805...826225754111 1963-05-11 Donald B. Gillies
M22 9,941 2,993 5,985 346088282490...883789463551 1963-05-16 Donald B. Gillies
M23 11,213 3,376 6,751 281411201369...087696392191 1963-06-02 Donald B. Gillies
M24 19,937 6,002 12,003 431542479738...030968041471 1971-03-04 Bryant Tuckerman
M25 21,701 6,533 13,066 448679166119...353511882751 1978-10-30 Landon Curt Noll, Laura A. Nickel
M26 23,209 6,987 13,973 402874115778...523779264511 1979-02-09 Landon Curt Noll
M27 44,497 13,395 26,790 854509824303...961011228671 1979-04-08 Harry Lewis Nelson, David Slowinski
M28 86,243 25,962 51,924 536927995502...709433438207 1982-09-25 David Slowinski
M29 110,503 33,265 66,530 521928313341...083465515007 1988-01-28 Walter Colquitt, Luke Welsh
M30 132,049 39,751 79,502 512740276269...455730061311 1983-09-19 David Slowinski
M31 216,091 65,050 130,100 746093103064...103815528447 1985-09-01 David Slowinski
M32 756,839 227,832 455,663 174135906820...328544677887 1992-02-19 David Slowinski, Paul Gage
M33 859,433 258,716 517,430 129498125604...243500142591 1994-01-04 David Slowinski, Paul Gage
M34 1,257,787 378,632 757,263 412245773621...976089366527 1996-09-03 David Slowinski, Paul Gage
M35 1,398,269 420,921 841,842 814717564412...868451315711 1996-11-13 Joel Armengaud, George Woltman et. al., GIMPS
M36 2,976,221 895,932 1,791,864 623340076248...743729201151 1997-08-24 Gordon Spence, George Woltman et. al., GIMPS
M37 3,021,377 909,526 1,819,050 127411683030...973024694271 1998-01-27 Roland Clarkson, George Woltman et. al., GIMPS
M38 6,972,593 2,098,960 4,197,919 437075744127...142924193791 1999-06-01 Nayan Hajratwala, George Woltman et. al., GIMPS
M39 13,466,917 4,053,946 8,107,892 924947738006...470256259071 2001-11-14 Michael Cameron, George Woltman et. al., GIMPS
M40 20,996,011 6,320,430 12,640,858 125976895450...762855682047 2003-11-17 Michael Shafer, George Woltman et. al., GIMPS
M41 24,036,583 7,235,733 14,471,465 299410429404...882733969407 2004-05-15 Josh Findley, George Woltman et. al., GIMPS
M42 25,964,951 7,816,230 15,632,458 122164630061...280577077247 2005-02-18 Martin Nowak, George Woltman et. al., GIMPS
M43 30,402,457 9,152,052 18,304,103 315416475618...411652943871 2005-12-15 Curtis Cooper, Steven Boone, George Woltman et. al., GIMPS
M44 32,582,657 9,808,358 19,616,714 124575026015...154053967871 2006-09-04 Curtis Cooper, Steven Boone, George Woltman et. al., GIMPS
M45 37,156,667 11,185,272 22,370,543 202254406890...022308220927 2008-09-06 Hans-Michael Elvenich, George Woltman et. al., GIMPS
M46 42,643,801 12,837,064 25,674,127 169873516452...765562314751 2009-04-12 Odd Magnar Strindmo, George Woltman et. al., GIMPS
M47 43,112,609 12,978,189 25,957,378 316470269330...166697152511 2008-08-23 Edson Smith, George Woltman, Scott Kurowski et al., (GIMPS & PrimeNet)
M48 57,885,161 17,425,170 34,850,340 581887266232...071724285951 2013-01-25 Curtis Cooper, George Woltman, Scott Kurowski, Aaron Blosser et. al., (GIMPS & PrimeNet)
M49* 74,207,281 22,338,618 44,677,236 300376418084...391086436351 2016-01-07 Curtis Cooper, George Woltman, Scott Kurowski, Aaron Blosser et. al., (GIMPS & PrimeNet)
M50* 77,232,917 23,249,425 46,498,850 467333183359...069762179071 2017-12-26 Jonathan Pace, George Woltman, Scott Kurowski, Aaron Blosser, (GIMPS & PrimeNet)
M51* 82,589,933 24,862,048 49,724,095 148894445742...325217902591 2018-12-07 Patrick Laroche, George Woltman, Aaron Blosser et. al., (GIMPS & PrimeNet)
M52* 136,279,841 41,024,320 82,048,640 881694327503...219486871551 2024-10-12 Luke Durant, Mihai Preda, George Woltman, Aaron Blosser et. al., (PRPLL/GpuOwL, GIMPS & PrimeNet)
* = Provisional ranking

See also

Mersenne prime

External links

Retrieved from "https://www.rieselprime.de/z/index.php?title=List_of_known_Mersenne_primes&oldid=1498"