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Difference between revisions of "List of known Mersenne primes"
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* ''M''<sub>''n''</sub> denotes the Mersenne prime <math>2^n{-}1</math> | * ''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> | * ''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" | ||
| Line 12: | Line 11: | ||
! Discoverer | ! Discoverer | ||
|- | |- | ||
| + | <!-- | ||
| align="right" | [[M1|1]] | | align="right" | [[M1|1]] | ||
| align="right" | 2 | | align="right" | 2 | ||
| Line 404: | Line 404: | ||
| align="right" | [[Curtis Cooper]], [[George Woltman]], [[Scott Kurowski]], [[Aaron Blosser]] et. al. [[GIMPS]] & [[PrimeNet]] | | align="right" | [[Curtis Cooper]], [[George Woltman]], [[Scott Kurowski]], [[Aaron Blosser]] et. al. [[GIMPS]] & [[PrimeNet]] | ||
|- | |- | ||
| + | --> | ||
| align="right" | [[M50|50]]<sup>*</sup> | | align="right" | [[M50|50]]<sup>*</sup> | ||
| align="right" | 77,232,917 | | align="right" | 77,232,917 | ||
| Line 420: | Line 421: | ||
| align="right" | [[Patrick Laroche]], [[George Woltman]], [[Aaron Blosser]] et. al. [[GIMPS]] & [[PrimeNet]] | | align="right" | [[Patrick Laroche]], [[George Woltman]], [[Aaron Blosser]] et. al. [[GIMPS]] & [[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 48th (M<sub>57 885 161</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. | ||
| Line 430: | Line 430: | ||
|order=ascending | |order=ascending | ||
|ordermethod=sortkey | |ordermethod=sortkey | ||
| − | |include={InfoboxMersennePrime}:title:nvalue:digits:pdigits:number:discovery:discoverer: | + | |include={InfoboxMersennePrime}:title:nvalue:digits:pdigits:number:discovery:discoverer,{InfoboxMersennePrime} dpl1,{InfoboxMersennePrime}:project:link2:link3 |
| − | |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,Credits,,, | + | |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,Credits,Poject,Link1,Link2 |
|tablerow=align=right{{!}}[[%%]],align=right{{!}}{{Num{{!}}%%}},align=right{{!}}{{Num{{!}}%%}},align=right{{!}}{{Num{{!}}%%}},align=center{{!}}%%,align=left{{!}}%%,%%,%%,%%,%% | |tablerow=align=right{{!}}[[%%]],align=right{{!}}{{Num{{!}}%%}},align=right{{!}}{{Num{{!}}%%}},align=right{{!}}{{Num{{!}}%%}},align=center{{!}}%%,align=left{{!}}%%,%%,%%,%%,%% | ||
}} | }} | ||
Revision as of 03:01, 16 February 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 |
|---|---|---|---|---|---|---|
| 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.
| # | n | Digits in Mn |
Digits in Pn |
Value of Mn |
Date | Discoverer | Credits | Poject | Link1 | Link2 |
|---|---|---|---|---|---|---|---|---|---|---|
| M50 | 77,232,917 | 23,249,425 | 46,498,850 | 467333183359...069762179071 | 2017-12-26 | Jonathan Pace | Template:InfoboxMersennePrime dpl1 | |||
| M51 | 82,589,933 | 24,862,048 | 49,724,095 | 148894445742...325217902591 | 2018-12-07 | Patrick Laroche | Template:InfoboxMersennePrime dpl1 |
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
