Talk:Lucas-Lehmer test: Difference between revisions
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m →List of known Mersenne primes: Got rid of wanted links to numbers, dates, and random people |
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:Yeah. I know. :-) --[[User:Short Circuit|Short Circuit]] 07:55, 21 February 2008 (MST) |
:Yeah. I know. :-) --[[User:Short Circuit|Short Circuit]] 07:55, 21 February 2008 (MST) |
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===List of known Mersenne primes=== |
===List of known Mersenne primes=== |
||
The table below lists all known Mersenne primes |
The table below lists all known Mersenne primes: |
||
{| class="wikitable" |
{| class="wikitable" |
||
|- |
|- |
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Line 15: | Line 15: | ||
| align="right" | 1 |
| align="right" | 1 |
||
| align="right" | 2 |
| align="right" | 2 |
||
| align="right" | |
| align="right" | 3 (number)|3 |
||
| align="right" | 1 |
| align="right" | 1 |
||
| ''ancient'' |
| ''ancient'' |
||
Line 22: | Line 22: | ||
| align="right" | 2 |
| align="right" | 2 |
||
| align="right" | 3 |
| align="right" | 3 |
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| align="right" | |
| align="right" | 7 (number)|7 |
||
| align="right" | 1 |
| align="right" | 1 |
||
| ''ancient'' |
| ''ancient'' |
||
Line 29: | Line 29: | ||
| align="right" | 3 |
| align="right" | 3 |
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| align="right" | 5 |
| align="right" | 5 |
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| align="right" | |
| align="right" | 31 (number)|31 |
||
| align="right" | 2 |
| align="right" | 2 |
||
| ''ancient'' |
| ''ancient'' |
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Line 36: | Line 36: | ||
| align="right" | 4 |
| align="right" | 4 |
||
| align="right" | 7 |
| align="right" | 7 |
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| align="right" | |
| align="right" | 127 (number)|127 |
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| align="right" | 3 |
| align="right" | 3 |
||
| ''ancient'' |
| ''ancient'' |
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Line 53: | Line 53: | ||
| align="right" | 6 |
| align="right" | 6 |
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| 1588 |
| 1588 |
||
| |
| Pietro Cataldi|Cataldi |
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|- |
|- |
||
| align="right" | 7 |
| align="right" | 7 |
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Line 60: | Line 60: | ||
| align="right" | 6 |
| align="right" | 6 |
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| 1588 |
| 1588 |
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| |
| Pietro Cataldi|Cataldi |
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|- |
|- |
||
| align="right" | 8 |
| align="right" | 8 |
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Line 67: | Line 67: | ||
| align="right" | 10 |
| align="right" | 10 |
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| 1772 |
| 1772 |
||
| |
| Leonhard Euler|Euler |
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|- |
|- |
||
| align="right" | 9 |
| align="right" | 9 |
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Line 74: | Line 74: | ||
| align="right" | 19 |
| align="right" | 19 |
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| 1883 |
| 1883 |
||
| |
| Ivan Mikheevich Pervushin|Pervushin |
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|- |
|- |
||
| align="right" | 10 |
| align="right" | 10 |
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Line 81: | Line 81: | ||
| align="right" | 27 |
| align="right" | 27 |
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| 1911 |
| 1911 |
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| |
| R. E. Powers|Powers |
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|- |
|- |
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| align="right" | 11 |
| align="right" | 11 |
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Line 88: | Line 88: | ||
| align="right" | 33 |
| align="right" | 33 |
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| 1914 |
| 1914 |
||
| |
| R. E. Powers|Powers[http://primes.utm.edu/notes/fauquem.html] |
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|- |
|- |
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| align="right" | 12 |
| align="right" | 12 |
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Line 95: | Line 95: | ||
| align="right" | 39 |
| align="right" | 39 |
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| 1876 |
| 1876 |
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| |
| Edouard Lucas|Lucas |
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|- |
|- |
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| align="right" | 13 |
| align="right" | 13 |
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Line 101: | Line 101: | ||
| align="right" | 686479766…115057151 |
| align="right" | 686479766…115057151 |
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| align="right" | 157 |
| align="right" | 157 |
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| |
| January 30 1952 |
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| |
| Raphael M. Robinson|Robinson |
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|- |
|- |
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| align="right" | 14 |
| align="right" | 14 |
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Line 108: | Line 108: | ||
| align="right" | 531137992…031728127 |
| align="right" | 531137992…031728127 |
||
| align="right" | 183 |
| align="right" | 183 |
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| |
| January 30 1952 |
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| |
| Raphael M. Robinson|Robinson |
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|- |
|- |
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| align="right" | 15 |
| align="right" | 15 |
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Line 115: | Line 115: | ||
| align="right" | 104079321…168729087 |
| align="right" | 104079321…168729087 |
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| align="right" | 386 |
| align="right" | 386 |
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| |
| June 25 1952 |
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| |
| Raphael M. Robinson|Robinson |
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|- |
|- |
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| align="right" | 16 |
| align="right" | 16 |
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Line 122: | Line 122: | ||
| align="right" | 147597991…697771007 |
| align="right" | 147597991…697771007 |
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| align="right" | 664 |
| align="right" | 664 |
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| |
| October 7 1952 |
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| |
| Raphael M. Robinson|Robinson |
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|- |
|- |
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| align="right" | 17 |
| align="right" | 17 |
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Line 129: | Line 129: | ||
| align="right" | 446087557…132836351 |
| align="right" | 446087557…132836351 |
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| align="right" | 687 |
| align="right" | 687 |
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| |
| October 9 1952 |
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| |
| Raphael M. Robinson|Robinson |
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|- |
|- |
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| align="right" | 18 |
| align="right" | 18 |
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Line 136: | Line 136: | ||
| align="right" | 259117086…909315071 |
| align="right" | 259117086…909315071 |
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| align="right" | 969 |
| align="right" | 969 |
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| |
| September 8 1957 |
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| |
| Hans Riesel|Riesel |
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|- |
|- |
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| align="right" | 19 |
| align="right" | 19 |
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Line 143: | Line 143: | ||
| align="right" | 190797007…350484991 |
| align="right" | 190797007…350484991 |
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| align="right" | 1,281 |
| align="right" | 1,281 |
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| |
| November 3 1961 |
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| |
| Alexander Hurwitz|Hurwitz |
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|- |
|- |
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| align="right" | 20 |
| align="right" | 20 |
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Line 150: | Line 150: | ||
| align="right" | 285542542…608580607 |
| align="right" | 285542542…608580607 |
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| align="right" | 1,332 |
| align="right" | 1,332 |
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| |
| November 3 1961 |
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| |
| Alexander Hurwitz|Hurwitz |
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|- |
|- |
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| align="right" | 21 |
| align="right" | 21 |
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Line 157: | Line 157: | ||
| align="right" | 478220278…225754111 |
| align="right" | 478220278…225754111 |
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| align="right" | 2,917 |
| align="right" | 2,917 |
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| |
| May 11 1963 |
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| |
| Donald B. Gillies|Gillies |
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|- |
|- |
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| align="right" | 22 |
| align="right" | 22 |
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Line 164: | Line 164: | ||
| align="right" | 346088282…789463551 |
| align="right" | 346088282…789463551 |
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| align="right" | 2,993 |
| align="right" | 2,993 |
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| |
| May 16 1963 |
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| |
| Donald B. Gillies|Gillies |
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|- |
|- |
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| align="right" | 23 |
| align="right" | 23 |
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Line 171: | Line 171: | ||
| align="right" | 281411201…696392191 |
| align="right" | 281411201…696392191 |
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| align="right" | 3,376 |
| align="right" | 3,376 |
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| |
| June 2 1963 |
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| |
| Donald B. Gillies|Gillies |
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|- |
|- |
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| align="right" | 24 |
| align="right" | 24 |
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Line 178: | Line 178: | ||
| align="right" | 431542479…968041471 |
| align="right" | 431542479…968041471 |
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| align="right" | 6,002 |
| align="right" | 6,002 |
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| |
| March 4 1971 |
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| |
| Bryant Tuckerman|Tuckerman |
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|- |
|- |
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| align="right" | 25 |
| align="right" | 25 |
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Line 185: | Line 185: | ||
| align="right" | 448679166…511882751 |
| align="right" | 448679166…511882751 |
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| align="right" | 6,533 |
| align="right" | 6,533 |
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| |
| October 30 1978 |
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| |
| Landon Curt Noll|Noll & Laura Nickel|Nickel |
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|- |
|- |
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| align="right" | 26 |
| align="right" | 26 |
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Line 192: | Line 192: | ||
| align="right" | 402874115…779264511 |
| align="right" | 402874115…779264511 |
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| align="right" | 6,987 |
| align="right" | 6,987 |
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| |
| February 9 1979 |
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| |
| Landon Curt Noll|Noll |
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|- |
|- |
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| align="right" | 27 |
| align="right" | 27 |
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Line 199: | Line 199: | ||
| align="right" | 854509824…011228671 |
| align="right" | 854509824…011228671 |
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| align="right" | 13,395 |
| align="right" | 13,395 |
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| |
| April 8 1979 |
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| |
| Harry Nelson|Nelson & David Slowinski|Slowinski |
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|- |
|- |
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| align="right" | 28 |
| align="right" | 28 |
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Line 206: | Line 206: | ||
| align="right" | 536927995…433438207 |
| align="right" | 536927995…433438207 |
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| align="right" | 25,962 |
| align="right" | 25,962 |
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| |
| September 25 1982 |
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| |
| David Slowinski|Slowinski |
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|- |
|- |
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| align="right" | 29 |
| align="right" | 29 |
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Line 213: | Line 213: | ||
| align="right" | 521928313…465515007 |
| align="right" | 521928313…465515007 |
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| align="right" | 33,265 |
| align="right" | 33,265 |
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| |
| January 28 1988 |
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| Walt Colquitt|Colquitt & Luke Welsh|Welsh |
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|- |
|- |
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| align="right" | 30 |
| align="right" | 30 |
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Line 220: | Line 220: | ||
| align="right" | 512740276…730061311 |
| align="right" | 512740276…730061311 |
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| align="right" | 39,751 |
| align="right" | 39,751 |
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| |
| September 19 1983[http://www.isthe.com/chongo/tech/math/prime/mersenne.html#largest] |
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| |
| David Slowinski|Slowinski |
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|- |
|- |
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| align="right" | 31 |
| align="right" | 31 |
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Line 227: | Line 227: | ||
| align="right" | 746093103…815528447 |
| align="right" | 746093103…815528447 |
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| align="right" | 65,050 |
| align="right" | 65,050 |
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| |
| September 1 1985[http://www.isthe.com/chongo/tech/math/prime/mersenne.html#largest] |
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| |
| David Slowinski|Slowinski |
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|- |
|- |
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| align="right" | 32 |
| align="right" | 32 |
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Line 234: | Line 234: | ||
| align="right" | 174135906…544677887 |
| align="right" | 174135906…544677887 |
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| align="right" | 227,832 |
| align="right" | 227,832 |
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| |
| February 19 1992 |
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| |
| David Slowinski|Slowinski & Paul Gage|Gage on Harwell Lab Cray-2 [http://primes.utm.edu/notes/756839.html] |
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|- |
|- |
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| align="right" | 33 |
| align="right" | 33 |
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Line 241: | Line 241: | ||
| align="right" | 129498125…500142591 |
| align="right" | 129498125…500142591 |
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| align="right" | 258,716 |
| align="right" | 258,716 |
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| |
| January 4 1994 [http://www.math.unicaen.fr/~reyssat/largest.html] |
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| |
| David Slowinski|Slowinski & Paul Gage|Gage |
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|- |
|- |
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| align="right" | 34 |
| align="right" | 34 |
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Line 248: | Line 248: | ||
| align="right" | 412245773…089366527 |
| align="right" | 412245773…089366527 |
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| align="right" | 378,632 |
| align="right" | 378,632 |
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| September 3 1996 |
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| |
| David Slowinski|Slowinski & Paul Gage|Gage [http://primes.utm.edu/notes/1257787.html] |
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|- |
|- |
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| align="right" | 35 |
| align="right" | 35 |
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Line 255: | Line 255: | ||
| align="right" | 814717564…451315711 |
| align="right" | 814717564…451315711 |
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| align="right" | 420,921 |
| align="right" | 420,921 |
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| November 13 1996 |
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| |
| Great Internet Mersenne Prime Search|GIMPS / Joel Armengaud [http://www.mersenne.org/1398269.htm] |
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|- |
|- |
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| align="right" | 36 |
| align="right" | 36 |
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Line 262: | Line 262: | ||
| align="right" | 623340076…729201151 |
| align="right" | 623340076…729201151 |
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| align="right" | 895,932 |
| align="right" | 895,932 |
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| August 24 1997 |
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| Great Internet Mersenne Prime Search|GIMPS / Gordon Spence [http://www.mersenne.org/2976221.htm] |
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|- |
|- |
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| align="right" | 37 |
| align="right" | 37 |
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Line 269: | Line 269: | ||
| align="right" | 127411683…024694271 |
| align="right" | 127411683…024694271 |
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| align="right" | 909,526 |
| align="right" | 909,526 |
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| January 27 1998 |
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| Great Internet Mersenne Prime Search|GIMPS / Roland Clarkson [http://www.mersenne.org/3021377.htm] |
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|- |
|- |
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| align="right" | 38 |
| align="right" | 38 |
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Line 276: | Line 276: | ||
| align="right" | 437075744…924193791 |
| align="right" | 437075744…924193791 |
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| align="right" | 2,098,960 |
| align="right" | 2,098,960 |
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| |
| June 1 1999 |
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| Great Internet Mersenne Prime Search|GIMPS / Nayan Hajratwala [http://www.mersenne.org/6972593.htm] |
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|- |
|- |
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| align="right" | 39 |
| align="right" | 39 |
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Line 283: | Line 283: | ||
| align="right" | 924947738…256259071 |
| align="right" | 924947738…256259071 |
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| align="right" | 4,053,946 |
| align="right" | 4,053,946 |
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| November 14 2001 |
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| Great Internet Mersenne Prime Search|GIMPS / Michael Cameron [http://www.mersenne.org/13466917.htm] |
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|- |
|- |
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| align="right" | 40<sup>*</sup> |
| align="right" | 40<sup>*</sup> |
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Line 290: | Line 290: | ||
| align="right" | 125976895…855682047 |
| align="right" | 125976895…855682047 |
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| align="right" | 6,320,430 |
| align="right" | 6,320,430 |
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| November 17 2003 |
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| Great Internet Mersenne Prime Search|GIMPS / Michael Shafer [http://www.mersenne.org/20996011.htm] |
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|- |
|- |
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| align="right" | 41<sup>*</sup> |
| align="right" | 41<sup>*</sup> |
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Line 297: | Line 297: | ||
| align="right" | 299410429…733969407 |
| align="right" | 299410429…733969407 |
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| align="right" | 7,235,733 |
| align="right" | 7,235,733 |
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| May 15 2004 |
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| Great Internet Mersenne Prime Search|GIMPS / Josh Findley [http://www.mersenne.org/24036583.htm] |
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|- |
|- |
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| align="right" | 42<sup>*</sup> |
| align="right" | 42<sup>*</sup> |
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Line 304: | Line 304: | ||
| align="right" | 122164630…577077247 |
| align="right" | 122164630…577077247 |
||
| align="right" | 7,816,230 |
| align="right" | 7,816,230 |
||
| |
| February 18 2005 |
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| Great Internet Mersenne Prime Search|GIMPS / Martin Nowak [http://www.mersenne.org/25964951.htm] |
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|- |
|- |
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| align="right" | 43<sup>*</sup> |
| align="right" | 43<sup>*</sup> |
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Line 311: | Line 311: | ||
| align="right" | 315416475…652943871 |
| align="right" | 315416475…652943871 |
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| align="right" | 9,152,052 |
| align="right" | 9,152,052 |
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| |
| December 15 2005 |
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| Great Internet Mersenne Prime Search|GIMPS / Curtis Cooper (mathematician)|Curtis Cooper & Steven Boone [http://www.mersenne.org/30402457.htm] |
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|- |
|- |
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| align="right" | 44<sup>*</sup> |
| align="right" | 44<sup>*</sup> |
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Line 318: | Line 318: | ||
| align="right" | 124575026…053967871 |
| align="right" | 124575026…053967871 |
||
| align="right" | 9,808,358 |
| align="right" | 9,808,358 |
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| |
| September 4 2006 |
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| |
| Great Internet Mersenne Prime Search|GIMPS / Curtis Cooper (mathematician)|Curtis Cooper & Steven Boone [http://www.mersenne.org/32582657.htm] |
||
|} |
|} |
||
Revision as of 20:24, 8 March 2008
M23,209 is 36 CPU hours ≡ 1979
Welcome to 1979!
- Yeah. I know. :-) --Short Circuit 07:55, 21 February 2008 (MST)
List of known Mersenne primes
The table below lists all known Mersenne primes:
# | n | Mn | Digits in Mn | Date of discovery | Discoverer |
---|---|---|---|---|---|
1 | 2 | 3 (number)|3 | 1 | ancient | ancient |
2 | 3 | 7 (number)|7 | 1 | ancient | ancient |
3 | 5 | 31 (number)|31 | 2 | ancient | ancient |
4 | 7 | 127 (number)|127 | 3 | ancient | ancient |
5 | 13 | 8191 | 4 | 1456 | anonymous [1] |
6 | 17 | 131071 | 6 | 1588 | Cataldi |
7 | 19 | 524287 | 6 | 1588 | Cataldi |
8 | 31 | 2147483647 | 10 | 1772 | Euler |
9 | 61 | 2305843009213693951 | 19 | 1883 | Pervushin |
10 | 89 | 618970019…449562111 | 27 | 1911 | Powers |
11 | 107 | 162259276…010288127 | 33 | 1914 | Powers[2] |
12 | 127 | 170141183…884105727 | 39 | 1876 | Lucas |
13 | 521 | 686479766…115057151 | 157 | January 30 1952 | Robinson |
14 | 607 | 531137992…031728127 | 183 | January 30 1952 | Robinson |
15 | 1,279 | 104079321…168729087 | 386 | June 25 1952 | Robinson |
16 | 2,203 | 147597991…697771007 | 664 | October 7 1952 | Robinson |
17 | 2,281 | 446087557…132836351 | 687 | October 9 1952 | Robinson |
18 | 3,217 | 259117086…909315071 | 969 | September 8 1957 | Riesel |
19 | 4,253 | 190797007…350484991 | 1,281 | November 3 1961 | Hurwitz |
20 | 4,423 | 285542542…608580607 | 1,332 | November 3 1961 | Hurwitz |
21 | 9,689 | 478220278…225754111 | 2,917 | May 11 1963 | Gillies |
22 | 9,941 | 346088282…789463551 | 2,993 | May 16 1963 | Gillies |
23 | 11,213 | 281411201…696392191 | 3,376 | June 2 1963 | Gillies |
24 | 19,937 | 431542479…968041471 | 6,002 | March 4 1971 | Tuckerman |
25 | 21,701 | 448679166…511882751 | 6,533 | October 30 1978 | Noll & Laura Nickel|Nickel |
26 | 23,209 | 402874115…779264511 | 6,987 | February 9 1979 | Noll |
27 | 44,497 | 854509824…011228671 | 13,395 | April 8 1979 | Nelson & David Slowinski|Slowinski |
28 | 86,243 | 536927995…433438207 | 25,962 | September 25 1982 | Slowinski |
29 | 110,503 | 521928313…465515007 | 33,265 | January 28 1988 | Colquitt & Luke Welsh|Welsh |
30 | 132,049 | 512740276…730061311 | 39,751 | September 19 1983[3] | Slowinski |
31 | 216,091 | 746093103…815528447 | 65,050 | September 1 1985[4] | Slowinski |
32 | 756,839 | 174135906…544677887 | 227,832 | February 19 1992 | Slowinski & Paul Gage|Gage on Harwell Lab Cray-2 [5] |
33 | 859,433 | 129498125…500142591 | 258,716 | January 4 1994 [6] | Slowinski & Paul Gage|Gage |
34 | 1,257,787 | 412245773…089366527 | 378,632 | September 3 1996 | Slowinski & Paul Gage|Gage [7] |
35 | 1,398,269 | 814717564…451315711 | 420,921 | November 13 1996 | GIMPS / Joel Armengaud [8] |
36 | 2,976,221 | 623340076…729201151 | 895,932 | August 24 1997 | GIMPS / Gordon Spence [9] |
37 | 3,021,377 | 127411683…024694271 | 909,526 | January 27 1998 | GIMPS / Roland Clarkson [10] |
38 | 6,972,593 | 437075744…924193791 | 2,098,960 | June 1 1999 | GIMPS / Nayan Hajratwala [11] |
39 | 13,466,917 | 924947738…256259071 | 4,053,946 | November 14 2001 | GIMPS / Michael Cameron [12] |
40* | 20,996,011 | 125976895…855682047 | 6,320,430 | November 17 2003 | GIMPS / Michael Shafer [13] |
41* | 24,036,583 | 299410429…733969407 | 7,235,733 | May 15 2004 | GIMPS / Josh Findley [14] |
42* | 25,964,951 | 122164630…577077247 | 7,816,230 | February 18 2005 | GIMPS / Martin Nowak [15] |
43* | 30,402,457 | 315416475…652943871 | 9,152,052 | December 15 2005 | GIMPS / Curtis Cooper (mathematician)|Curtis Cooper & Steven Boone [16] |
44* | 32,582,657 | 124575026…053967871 | 9,808,358 | September 4 2006 | GIMPS / Curtis Cooper (mathematician)|Curtis Cooper & Steven Boone [17] |
Java precision
The Java version is still limited by types. Integer.parseInt(args[0]) limits p to 2147483647. Also the fact that isMersennePrime takes an int limits it there too. For full arbitrary precision every int needs to be a BigInteger or BigDecimal and a square root method will need to be created for them. The limitation is OK I think (I don't think we'll be getting up to 22147483647 - 1 anytime soon), but the claim "any arbitrary prime" is false because of the use of ints. --Mwn3d 07:45, 21 February 2008 (MST)