Talk:Lucas-Lehmer test: Difference between revisions

Content added Content deleted
m (→‎List of known Mersenne primes: Got rid of wanted links to numbers, dates, and random people)
Line 3: Line 3:
: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)
===List of known Mersenne primes===
===List of known Mersenne primes===
The table below lists all known Mersenne primes {{OEIS|id=A000668}}:
The table below lists all known Mersenne primes:
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 15: Line 15:
| align="right" | 1
| align="right" | 1
| align="right" | 2
| align="right" | 2
| align="right" | [[3 (number)|3]]
| 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
| align="right" | [[7 (number)|7]]
| align="right" | 7 (number)|7
| align="right" | 1
| align="right" | 1
| ''ancient''
| ''ancient''
Line 29: Line 29:
| align="right" | 3
| align="right" | 3
| align="right" | 5
| align="right" | 5
| align="right" | [[31 (number)|31]]
| align="right" | 31 (number)|31
| align="right" | 2
| align="right" | 2
| ''ancient''
| ''ancient''
Line 36: Line 36:
| align="right" | 4
| align="right" | 4
| align="right" | 7
| align="right" | 7
| align="right" | [[127 (number)|127]]
| align="right" | 127 (number)|127
| align="right" | 3
| align="right" | 3
| ''ancient''
| ''ancient''
Line 53: Line 53:
| align="right" | 6
| align="right" | 6
| 1588
| 1588
| [[Pietro Cataldi|Cataldi]]
| Pietro Cataldi|Cataldi
|-
|-
| align="right" | 7
| align="right" | 7
Line 60: Line 60:
| align="right" | 6
| align="right" | 6
| 1588
| 1588
| [[Pietro Cataldi|Cataldi]]
| Pietro Cataldi|Cataldi
|-
|-
| align="right" | 8
| align="right" | 8
Line 67: Line 67:
| align="right" | 10
| align="right" | 10
| 1772
| 1772
| [[Leonhard Euler|Euler]]
| Leonhard Euler|Euler
|-
|-
| align="right" | 9
| align="right" | 9
Line 74: Line 74:
| align="right" | 19
| align="right" | 19
| 1883
| 1883
| [[Ivan Mikheevich Pervushin|Pervushin]]
| Ivan Mikheevich Pervushin|Pervushin
|-
|-
| align="right" | 10
| align="right" | 10
Line 81: Line 81:
| align="right" | 27
| align="right" | 27
| 1911
| 1911
| [[R. E. Powers|Powers]]
| R. E. Powers|Powers
|-
|-
| align="right" | 11
| align="right" | 11
Line 88: Line 88:
| align="right" | 33
| align="right" | 33
| 1914
| 1914
| [[R. E. Powers|Powers]][http://primes.utm.edu/notes/fauquem.html]
| R. E. Powers|Powers[http://primes.utm.edu/notes/fauquem.html]
|-
|-
| align="right" | 12
| align="right" | 12
Line 95: Line 95:
| align="right" | 39
| align="right" | 39
| 1876
| 1876
| [[Edouard Lucas|Lucas]]
| Edouard Lucas|Lucas
|-
|-
| align="right" | 13
| align="right" | 13
Line 101: Line 101:
| align="right" | 686479766…115057151
| align="right" | 686479766…115057151
| align="right" | 157
| align="right" | 157
| [[January 30]] [[1952]]
| January 30 1952
| [[Raphael M. Robinson|Robinson]]
| Raphael M. Robinson|Robinson
|-
|-
| align="right" | 14
| align="right" | 14
Line 108: Line 108:
| align="right" | 531137992…031728127
| align="right" | 531137992…031728127
| align="right" | 183
| align="right" | 183
| [[January 30]] [[1952]]
| January 30 1952
| [[Raphael M. Robinson|Robinson]]
| Raphael M. Robinson|Robinson
|-
|-
| align="right" | 15
| align="right" | 15
Line 115: Line 115:
| align="right" | 104079321…168729087
| align="right" | 104079321…168729087
| align="right" | 386
| align="right" | 386
| [[June 25]] [[1952]]
| June 25 1952
| [[Raphael M. Robinson|Robinson]]
| Raphael M. Robinson|Robinson
|-
|-
| align="right" | 16
| align="right" | 16
Line 122: Line 122:
| align="right" | 147597991…697771007
| align="right" | 147597991…697771007
| align="right" | 664
| align="right" | 664
| [[October 7]] [[1952]]
| October 7 1952
| [[Raphael M. Robinson|Robinson]]
| Raphael M. Robinson|Robinson
|-
|-
| align="right" | 17
| align="right" | 17
Line 129: Line 129:
| align="right" | 446087557…132836351
| align="right" | 446087557…132836351
| align="right" | 687
| align="right" | 687
| [[October 9]] [[1952]]
| October 9 1952
| [[Raphael M. Robinson|Robinson]]
| Raphael M. Robinson|Robinson
|-
|-
| align="right" | 18
| align="right" | 18
Line 136: Line 136:
| align="right" | 259117086…909315071
| align="right" | 259117086…909315071
| align="right" | 969
| align="right" | 969
| [[September 8]] [[1957]]
| September 8 1957
| [[Hans Riesel|Riesel]]
| Hans Riesel|Riesel
|-
|-
| align="right" | 19
| align="right" | 19
Line 143: Line 143:
| align="right" | 190797007…350484991
| align="right" | 190797007…350484991
| align="right" | 1,281
| align="right" | 1,281
| [[November 3]] [[1961]]
| November 3 1961
| [[Alexander Hurwitz|Hurwitz]]
| Alexander Hurwitz|Hurwitz
|-
|-
| align="right" | 20
| align="right" | 20
Line 150: Line 150:
| align="right" | 285542542…608580607
| align="right" | 285542542…608580607
| align="right" | 1,332
| align="right" | 1,332
| [[November 3]] [[1961]]
| November 3 1961
| [[Alexander Hurwitz|Hurwitz]]
| Alexander Hurwitz|Hurwitz
|-
|-
| align="right" | 21
| align="right" | 21
Line 157: Line 157:
| align="right" | 478220278…225754111
| align="right" | 478220278…225754111
| align="right" | 2,917
| align="right" | 2,917
| [[May 11]] [[1963]]
| May 11 1963
| [[Donald B. Gillies|Gillies]]
| Donald B. Gillies|Gillies
|-
|-
| align="right" | 22
| align="right" | 22
Line 164: Line 164:
| align="right" | 346088282…789463551
| align="right" | 346088282…789463551
| align="right" | 2,993
| align="right" | 2,993
| [[May 16]] [[1963]]
| May 16 1963
| [[Donald B. Gillies|Gillies]]
| Donald B. Gillies|Gillies
|-
|-
| align="right" | 23
| align="right" | 23
Line 171: Line 171:
| align="right" | 281411201…696392191
| align="right" | 281411201…696392191
| align="right" | 3,376
| align="right" | 3,376
| [[June 2]] [[1963]]
| June 2 1963
| [[Donald B. Gillies|Gillies]]
| Donald B. Gillies|Gillies
|-
|-
| align="right" | 24
| align="right" | 24
Line 178: Line 178:
| align="right" | 431542479…968041471
| align="right" | 431542479…968041471
| align="right" | 6,002
| align="right" | 6,002
| [[March 4]] [[1971]]
| March 4 1971
| [[Bryant Tuckerman|Tuckerman]]
| Bryant Tuckerman|Tuckerman
|-
|-
| align="right" | 25
| align="right" | 25
Line 185: Line 185:
| align="right" | 448679166…511882751
| align="right" | 448679166…511882751
| align="right" | 6,533
| align="right" | 6,533
| [[October 30]] [[1978]]
| October 30 1978
| [[Landon Curt Noll|Noll]] & [[Laura Nickel|Nickel]]
| Landon Curt Noll|Noll & Laura Nickel|Nickel
|-
|-
| align="right" | 26
| align="right" | 26
Line 192: Line 192:
| align="right" | 402874115…779264511
| align="right" | 402874115…779264511
| align="right" | 6,987
| align="right" | 6,987
| [[February 9]] [[1979]]
| February 9 1979
| [[Landon Curt Noll|Noll]]
| Landon Curt Noll|Noll
|-
|-
| align="right" | 27
| align="right" | 27
Line 199: Line 199:
| align="right" | 854509824…011228671
| align="right" | 854509824…011228671
| align="right" | 13,395
| align="right" | 13,395
| [[April 8]] [[1979]]
| April 8 1979
| [[Harry Nelson|Nelson]] & [[David Slowinski|Slowinski]]
| Harry Nelson|Nelson & David Slowinski|Slowinski
|-
|-
| align="right" | 28
| align="right" | 28
Line 206: Line 206:
| align="right" | 536927995…433438207
| align="right" | 536927995…433438207
| align="right" | 25,962
| align="right" | 25,962
| [[September 25]] [[1982]]
| September 25 1982
| [[David Slowinski|Slowinski]]
| David Slowinski|Slowinski
|-
|-
| align="right" | 29
| align="right" | 29
Line 213: Line 213:
| align="right" | 521928313…465515007
| align="right" | 521928313…465515007
| align="right" | 33,265
| align="right" | 33,265
| [[January 28]] [[1988]]
| January 28 1988
| [[Walt Colquitt|Colquitt]] & [[Luke Welsh|Welsh]]
| Walt Colquitt|Colquitt & Luke Welsh|Welsh
|-
|-
| align="right" | 30
| align="right" | 30
Line 220: Line 220:
| align="right" | 512740276…730061311
| align="right" | 512740276…730061311
| align="right" | 39,751
| align="right" | 39,751
| [[September 19]] [[1983]][http://www.isthe.com/chongo/tech/math/prime/mersenne.html#largest]
| September 19 1983[http://www.isthe.com/chongo/tech/math/prime/mersenne.html#largest]
| [[David Slowinski|Slowinski]]
| David Slowinski|Slowinski
|-
|-
| align="right" | 31
| align="right" | 31
Line 227: Line 227:
| align="right" | 746093103…815528447
| align="right" | 746093103…815528447
| align="right" | 65,050
| align="right" | 65,050
| [[September 1]] [[1985]][http://www.isthe.com/chongo/tech/math/prime/mersenne.html#largest]
| September 1 1985[http://www.isthe.com/chongo/tech/math/prime/mersenne.html#largest]
| [[David Slowinski|Slowinski]]
| David Slowinski|Slowinski
|-
|-
| align="right" | 32
| align="right" | 32
Line 234: Line 234:
| align="right" | 174135906…544677887
| align="right" | 174135906…544677887
| align="right" | 227,832
| align="right" | 227,832
| [[February 19]] [[1992]]
| February 19 1992
| [[David Slowinski|Slowinski]] & [[Paul Gage|Gage]] on [[Harwell Lab]] [[Cray-2]] [http://primes.utm.edu/notes/756839.html]
| David Slowinski|Slowinski & Paul Gage|Gage on Harwell Lab Cray-2 [http://primes.utm.edu/notes/756839.html]
|-
|-
| align="right" | 33
| align="right" | 33
Line 241: Line 241:
| align="right" | 129498125…500142591
| align="right" | 129498125…500142591
| align="right" | 258,716
| align="right" | 258,716
| [[January 4]] [[1994]] [http://www.math.unicaen.fr/~reyssat/largest.html]
| January 4 1994 [http://www.math.unicaen.fr/~reyssat/largest.html]
| [[David Slowinski|Slowinski]] & [[Paul Gage|Gage]]
| David Slowinski|Slowinski & Paul Gage|Gage
|-
|-
| align="right" | 34
| align="right" | 34
Line 248: Line 248:
| align="right" | 412245773…089366527
| align="right" | 412245773…089366527
| align="right" | 378,632
| align="right" | 378,632
| [[September 3]] [[1996]]
| September 3 1996
| [[David Slowinski|Slowinski]] & [[Paul Gage|Gage]] [http://primes.utm.edu/notes/1257787.html]
| David Slowinski|Slowinski & Paul Gage|Gage [http://primes.utm.edu/notes/1257787.html]
|-
|-
| align="right" | 35
| align="right" | 35
Line 255: Line 255:
| align="right" | 814717564…451315711
| align="right" | 814717564…451315711
| align="right" | 420,921
| align="right" | 420,921
| [[November 13]] [[1996]]
| November 13 1996
| [[Great Internet Mersenne Prime Search|GIMPS]] / Joel Armengaud [http://www.mersenne.org/1398269.htm]
| Great Internet Mersenne Prime Search|GIMPS / Joel Armengaud [http://www.mersenne.org/1398269.htm]
|-
|-
| align="right" | 36
| align="right" | 36
Line 262: Line 262:
| align="right" | 623340076…729201151
| align="right" | 623340076…729201151
| align="right" | 895,932
| align="right" | 895,932
| [[August 24]] [[1997]]
| August 24 1997
| [[Great Internet Mersenne Prime Search|GIMPS]] / Gordon Spence [http://www.mersenne.org/2976221.htm]
| Great Internet Mersenne Prime Search|GIMPS / Gordon Spence [http://www.mersenne.org/2976221.htm]
|-
|-
| align="right" | 37
| align="right" | 37
Line 269: Line 269:
| align="right" | 127411683…024694271
| align="right" | 127411683…024694271
| align="right" | 909,526
| align="right" | 909,526
| [[January 27]] [[1998]]
| January 27 1998
| [[Great Internet Mersenne Prime Search|GIMPS]] / Roland Clarkson [http://www.mersenne.org/3021377.htm]
| Great Internet Mersenne Prime Search|GIMPS / Roland Clarkson [http://www.mersenne.org/3021377.htm]
|-
|-
| align="right" | 38
| align="right" | 38
Line 276: Line 276:
| align="right" | 437075744…924193791
| align="right" | 437075744…924193791
| align="right" | 2,098,960
| align="right" | 2,098,960
| [[June 1]] [[1999]]
| June 1 1999
| [[Great Internet Mersenne Prime Search|GIMPS]] / Nayan Hajratwala [http://www.mersenne.org/6972593.htm]
| Great Internet Mersenne Prime Search|GIMPS / Nayan Hajratwala [http://www.mersenne.org/6972593.htm]
|-
|-
| align="right" | 39
| align="right" | 39
Line 283: Line 283:
| align="right" | 924947738…256259071
| align="right" | 924947738…256259071
| align="right" | 4,053,946
| align="right" | 4,053,946
| [[November 14]] [[2001]]
| November 14 2001
| [[Great Internet Mersenne Prime Search|GIMPS]] / Michael Cameron [http://www.mersenne.org/13466917.htm]
| Great Internet Mersenne Prime Search|GIMPS / Michael Cameron [http://www.mersenne.org/13466917.htm]
|-
|-
| align="right" | 40<sup>*</sup>
| align="right" | 40<sup>*</sup>
Line 290: Line 290:
| align="right" | 125976895…855682047
| align="right" | 125976895…855682047
| align="right" | 6,320,430
| align="right" | 6,320,430
| [[November 17]] [[2003]]
| November 17 2003
| [[Great Internet Mersenne Prime Search|GIMPS]] / Michael Shafer [http://www.mersenne.org/20996011.htm]
| Great Internet Mersenne Prime Search|GIMPS / Michael Shafer [http://www.mersenne.org/20996011.htm]
|-
|-
| align="right" | 41<sup>*</sup>
| align="right" | 41<sup>*</sup>
Line 297: Line 297:
| align="right" | 299410429…733969407
| align="right" | 299410429…733969407
| align="right" | 7,235,733
| align="right" | 7,235,733
| [[May 15]] [[2004]]
| May 15 2004
| [[Great Internet Mersenne Prime Search|GIMPS]] / Josh Findley [http://www.mersenne.org/24036583.htm]
| Great Internet Mersenne Prime Search|GIMPS / Josh Findley [http://www.mersenne.org/24036583.htm]
|-
|-
| align="right" | 42<sup>*</sup>
| align="right" | 42<sup>*</sup>
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]]
| February 18 2005
| [[Great Internet Mersenne Prime Search|GIMPS]] / Martin Nowak [http://www.mersenne.org/25964951.htm]
| Great Internet Mersenne Prime Search|GIMPS / Martin Nowak [http://www.mersenne.org/25964951.htm]
|-
|-
| align="right" | 43<sup>*</sup>
| align="right" | 43<sup>*</sup>
Line 311: Line 311:
| align="right" | 315416475…652943871
| align="right" | 315416475…652943871
| align="right" | 9,152,052
| align="right" | 9,152,052
| [[December 15]] [[2005]]
| December 15 2005
| [[Great Internet Mersenne Prime Search|GIMPS]] / [[Curtis Cooper (mathematician)|Curtis Cooper]] & [[Steven Boone]] [http://www.mersenne.org/30402457.htm]
| Great Internet Mersenne Prime Search|GIMPS / Curtis Cooper (mathematician)|Curtis Cooper & Steven Boone [http://www.mersenne.org/30402457.htm]
|-
|-
| align="right" | 44<sup>*</sup>
| align="right" | 44<sup>*</sup>
Line 318: Line 318:
| align="right" | 124575026…053967871
| align="right" | 124575026…053967871
| align="right" | 9,808,358
| align="right" | 9,808,358
| [[September 4]] [[2006]]
| September 4 2006
| [[Great Internet Mersenne Prime Search|GIMPS]] / [[Curtis Cooper (mathematician)|Curtis Cooper]] & [[Steven Boone]] [http://www.mersenne.org/32582657.htm]
| Great Internet Mersenne Prime Search|GIMPS / Curtis Cooper (mathematician)|Curtis Cooper & Steven Boone [http://www.mersenne.org/32582657.htm]
|}
|}