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Difference between revisions of "List of known Mersenne primes"
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* [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) | ||
* [https://en.wikipedia.org/wiki/Mersenne_prime Wikipedia] | * [https://en.wikipedia.org/wiki/Mersenne_prime Wikipedia] | ||
| − | + | [[Category:Mersenne primes]] | |
| − | [[Category: | ||
Revision as of 15:18, 15 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
External links
- List of known Mersenne prime numbers at Mersenne.org
- prime Mersenne Numbers - History, Theorems and Lists Explanation
- GIMPS Mersenne Prime - status page gives various statistics on search progress, some parts are updated automatically, others typically updated every week, including progress towards proving the ordering of primes 41-47ff
- Mersenne numbers - Wolfram Research/Mathematica
- prime Mersenne numbers - Wolfram Research/Mathematica
- Mq = (8x)^2 - (3qy)^2 Mersenne Proof (pdf)
- Mq = x^2 + d.y^2 Math Thesis (pdf)
- Mersenne Prime Bibliography with Hyperlinks to original publications
- dpa - reportage about prime mersenne number - detection in detail (German)
- Wikipedia
