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Difference between revisions of "List of known Mersenne primes"

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(new, M51 added)
 
(corrected)
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* ''M''<sub>''n''</sub> denotes the Mersenne prime <math>2^n{-}1</math>
 +
* ''P''<sub>''n''</sub> denotes the Perfect number <math>2^{n-1}\cdot(2^n{-}1)</math>
 +
 
{| cellpadding="4" border="1" style="margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
 
{| cellpadding="4" border="1" style="margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
 
|- bgcolor="lightblue"
 
|- bgcolor="lightblue"
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| align="right" | [https://www.mersenne.org/primes/perfect/perfect82589933.zip 49,724,095]
 
| align="right" | [https://www.mersenne.org/primes/perfect/perfect82589933.zip 49,724,095]
 
| align="right" | 148894445742...325217902591
 
| align="right" | 148894445742...325217902591
−
| align="right" | [https://www.mersenne.org/primes/?press=M82589933 2017-12-26]
+
| 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]]
 
| 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
 
<sup>*</sup>It is not known whether any undiscovered Mersenne primes exist
−
between the 47th (M<sub>43,112,609</sub>) and the 51th (M<sub>82,589,933</sub>) on this chart; the ranking is therefore provisional.
+
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.
  
 
==See also==
 
==See also==

Revision as of 16:23, 14 January 2019

  • Mn denotes the Mersenne prime [math]\displaystyle{ 2^n{-}1 }[/math]
  • Pn denotes the Perfect number [math]\displaystyle{ 2^{n-1}\cdot(2^n{-}1) }[/math]
# n Digits in Mn Digits in Pn Value of Mn Date of
discovery 		Discoverer
1 2 1 1 3 c. 430 BCE Ancient Greek mathematicians
2 3 1 2 7 c. 430 BCE Ancient Greek mathematicians
3 5 2 3 31 c. 300 BCE Ancient Greek mathematicians
4 7 3 4 127 c. 300 BCE Ancient Greek mathematicians
5 13 4 8 8191 1456 anonymous
6 17 6 10 131071 1588 Cataldi
7 19 6 12 524287 1588 Cataldi
8 31 10 19 2147483647 1772 Leonhard Euler
9 61 19 37 2305843009213693951 1883 Ivan Mikheevich Pervushin
10 89 27 54 618970019642...137449562111 1911 Powers
11 107 33 65 162259276829...578010288127 1914 Powers
12 127 39 77 170141183460...715884105727 1876 Edouard Lucas
13 521 157 314 686479766013...291115057151 1952-01-30 Raphael Robinson
14 607 183 366 531137992816...219031728127 1952-01-30 Raphael Robinson
15 1,279 386 770 104079321946...703168729087 1952-06-25 Raphael Robinson
16 2,203 664 1,327 147597991521...686697771007 1952-10-07 Raphael Robinson
17 2,281 687 1,373 446087557183...418132836351 1952-11-09 Raphael Robinson
18 3,217 969 1,937 259117086013...362909315071 1957-09-08 Hans Riesel
19 4,253 1,281 2,561 190797007524...815350484991 1961-11-03 Hurwitz
20 4,423 1,332 2,663 285542542228...902608580607 1961-11-03 Hurwitz
21 9,689 2,917 5,834 478220278805...826225754111 1963-05-11 Gillies
22 9,941 2,993 5,985 346088282490...883789463551 1963-05-16 Gillies
23 11,213 3,376 6,751 281411201369...087696392191 1963-06-02 Gillies
24 19,937 6,002 12,003 431542479738...030968041471 1971-03-04 Tuckerman
25 21,701 6,533 13,066 448679166119...353511882751 1978-10-30 Landon Curt Noll & Laura A. Nickel
26 23,209 6,987 13,973 402874115778...523779264511 1979-02-09 Landon Curt Noll
27 44,497 13,395 26,790 854509824303...961011228671 1979-04-08 Nelson & David Slowinski
28 86,243 25,962 51,924 536927995502...709433438207 1982-09-25 David Slowinski
29 110,503 33,265 66,530 521928313341...083465515007 1988-01-28 Colquitt & Welsh
30 132,049 39,751 79,502 512740276269...455730061311 1983-09-20 David Slowinski
31 216,091 65,050 130,100 746093103064...103815528447 1985-09-06 David Slowinski
32 756,839 227,832 455,663 174135906820...328544677887 1992-02-19 David Slowinski, Paul Gage & Harwell
33 859,433 258,716 517,430 129498125604...243500142591 1994-01-10 David Slowinski & Paul Gage
34 1,257,787 378,632 757,263 412245773621...976089366527 1996-09-03 David Slowinski & Paul Gage
35 1,398,269 420,921 841,842 814717564412...868451315711 1996-11-13 Joel Armengaud, George Woltman et. al. GIMPS
36 2,976,221 895,932 1,791,864 623340076248...743729201151 1997-08-24 Gordon Spence, George Woltman et. al. GIMPS
37 3,021,377 909,526 1,819,050 127411683030...973024694271 1998-01-27 Roland Clarkson, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
38 6,972,593 2,098,960 4,197,919 437075744127...142924193791 1999-06-01 Nayan Hajratwala, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
39 13,466,917 4,053,946 8,107,892 924947738006...470256259071 2001-11-14 Michael Cameron, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
40 20,996,011 6,320,430 12,640,858 125976895450...762855682047 2003-11-17 Michael Shafer, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
41 24,036,583 7,235,733 14,471,465 299410429404...882733969407 2004-05-15 Josh Findley, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
42 25,964,951 7,816,230 15,632,458 122164630061...280577077247 2005-02-18 Martin Nowak, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
43 30,402,457 9,152,052 18,304,103 315416475618...411652943871 2005-12-15 Curtis Cooper, Steven Boone, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
44 32,582,657 9,808,358 19,616,714 124575026015...154053967871 2006-09-04 Curtis Cooper, Steven Boone, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
45 37,156,667 11,185,272 22,370,543 202254406890...022308220927 2008-09-06 Hans-Michael Elvenich, George Woltman, Scott Kurowski, et al. GIMPS & PrimeNet
46 42,643,801 12,837,064 25,674,127 169873516452...765562314751 2009-04-12 Odd M. Strindmo, George Woltman, Scott Kurowski, et al. GIMPS & PrimeNet
47 43,112,609 12,978,189 25,957,378 316470269330...166697152511 2008-08-23 Edson Smith, George Woltman, Scott Kurowski, et al. GIMPS & PrimeNet
48* 57,885,161 17,425,170 34,850,340 581887266232...071724285951 2013-01-25 Curtis Cooper, George Woltman, Scott Kurowski et. al. GIMPS & PrimeNet
49* 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
50* 77,232,917 23,249,425 46,498,850 467333183359...069762179071 2017-12-26 Jonathan Pace, George Woltman, Scott Kurowski, Aaron Blosser et. al. GIMPS & PrimeNet
51* 82,589,933 24,862,048 49,724,095 148894445742...325217902591 2018-12-07 Patrick Laroche, George Woltman, Aaron Blosser et. al. GIMPS & PrimeNet

*It is not known whether any undiscovered Mersenne primes exist between the 48th (M57,885,161) and the 51th (M82,589,933) on this chart; the ranking is therefore provisional.

See also

Mersenne prime

External links

Retrieved from "https://www.rieselprime.de/z/index.php?title=List_of_known_Mersenne_primes&oldid=181"