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Old 2008-01-01, 03:37   #1
Kosmaj
 
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Nov 2003

2·1,811 Posts
Default k*2^n-1 primes in 2007

Here is the list of 100 largest known primes of form k*2^n-1, k>=3 at the end of 2007. Based on the Top-5000 list maintained by prof. Caldwell.

Ranking:
r1, rank among k*2^n-1, k>=3
r2, rank among all known primes

Code:
-------------------------------------------------------------------------
 r1   r2    description                digits   who  year  comment
-------------------------------------------------------------------------
  1   13  938237*2^3752950-1          1129757  L521  2007  Woodall
  2   15  3*2^3136255-1                944108  L256  2007  
  3   22  342673*2^2639439-1           794556   L53  2007  
  4   25  26773*2^2465343-1            742147  L197  2006  
  5   26  737*2^2382804-1              717299  L191  2007  
  6   27  1183953*2^2367907-1          712818  L447  2007  Woodall
  7   28  275293*2^2335007-1           702913  L193  2006  
  8   29  3*2^2312734-1                696203  L158  2005  
  9   30  450457*2^2307905-1           694755  L172  2006  
 10   33  114487*2^2198389-1           661787  L179  2006  
 11   34  196597*2^2178109-1           655682  L175  2006  
 12   39  121*2^2033941-1              612280  L162  2006  
 13   40  251749*2^2013995-1           606279  L436  2007  Woodall
 14   41  467917*2^1993429-1           600088  L160  2005  
 15   42  137137*2^1993201-1           600019  L321  2007  
 16   44  121*2^1954243-1              588288  L162  2006  
 17   46  345067*2^1876573-1           564911   g59  2005  
 18   48  137*2^1849238-1              556679  L321  2007  
 19   51  417643*2^1800787-1           542097  L134  2005  
 20   52  357659*2^1779748-1           535764   L47  2005  
 21   54  253*2^1722623-1              518564  L145  2007  rps
 22   55  121*2^1695499-1              510399   L62  2005  
 23   58  469949*2^1649228-1           496473  L160  2007  
 24   61  58753*2^1594323-1            479944  p190  2006  
 25   62  737*2^1592724-1              479461  L191  2006  
 26   63  110413*2^1591999-1           479245  L111  2005  
 27   65  121*2^1589157-1              478387   L65  2005  
 28   72  234847*2^1535589-1           462264   L73  2005  
 29   73  121*2^1526097-1              459404   L65  2005  
 30   76  2232007*2^1490605-1          448724    L4  2003  
 31   77  29*2^1478344-1               445028   L10  2005  
 32   79  325627*2^1472117-1           443157  L111  2005  
 33   80  1467763*2^1467763-1          441847  L381  2007  Woodall
 34   81  77*2^1467554-1               441780  L145  2006  rps
 35   85  149797*2^1414137-1           425703  L105  2005  
 36   87  192089*2^1395688-1           420150   L49  2004  
 37   95  15*2^1344313-1               404680  L139  2007  rps
 38  109  138847*2^1283793-1           386466    L2  2003  
 39  112  1268979*2^1268979-1          382007  L201  2007  Woodall
 40  114  11*2^1261478-1               379744  L163  2006  rps
 41  116  26869*2^1257787-1            378637  L466  2007  
 42  119  80857169*2^1251076-1         376620   L10  2004  
 43  126  3*2^1232255-1                370947   L30  2004  
 44  132  3*2^1201046-1                361552   L77  2004  
 45  133  502541*2^1199930-1           361221   L93  2004  
 46  134  1195203*2^1195203-1          359799  L124  2005  Woodall
 47  137  71009*2^1185112-1            356760   L47  2004  
 48  139  617*2^1175468-1              353854  L426  2007  rps
 49  142  152713*2^1154707-1           347607   g23  2004  
 50  145  350107*2^1144101-1           344415   L35  2004  
 51  146  209826493*2^1140855-1        343440   L10  2004  
 52  147  500621*2^1138518-1           342734   L73  2004  
 53  148  504613*2^1136459-1           342114   L84  2004  
 54  154  99*2^1106989-1               333239  L486  2007  rps
 55  155  11*2^1104606-1               332521   L10  2005  
 56  157  289*2^1098117-1              330569    L6  2006  
 57  160  412717*2^1084409-1           326446   L76  2004  
 58  161  15*2^1084010-1               326321  L139  2006  rps
 59  162  150847*2^1076441-1           324047   L73  2004  
 60  164  209826493*2^1071303-1        322503   L10  2004  
 61  165  2203*2^1069647-1             322000  L123  2006  
 62  166  864316301*2^1055106-1        317628  L426  2007  rps
 63  168  11*2^1044086-1               314303   L10  2005  
 64  169  151515*2^1043018-1           313985  L426  2007  rps
 65  171  121*2^1039965-1              313063   L65  2004  
 66  173  85*2^1034069-1               311288  L323  2007  rps
 67  178  6119*2^1011416-1             304471  L251  2007  rps
 68  179  9*2^1010277-1                304125   L80  2007  
 69  188  21*2^999599-1                300911   L56  2005  
 70  190  1515*2^996848-1              300085  L200  2007  rps
 71  191  351351*2^996709-1            300045   L80  2006  
 72  193  3*2^992700-1                 298833   L59  2004  
 73  195  121*2^990219-1               298088   L66  2004  
 74  196  21*2^986130-1                296857   L56  2005  
 75  197  137137*2^978229-1            294482  L321  2007  
 76  198  69*2^978209-1                294473  L260  2007  rps
 77  204  111*2^959671-1               288892  L282  2007  rps
 78  205  231*2^959375-1               288804  L138  2006  rps
 79  206  1515*2^955219-1              287553  L200  2007  rps
 80  207  247*2^952069-1               286604  L138  2006  rps
 81  209  12345*2^948054-1             285397  L200  2007  rps
 82  210  87*2^942790-1                283811  L145  2006  rps
 83  211  25*2^942563-1                283742  L183  2006  rps
 84  213  246419198025*2^935249-1      281550  L106  2007  
 85  216  243163663*2^919087-1         276682   L10  2004  
 86  217  125*2^918494-1               276497  L384  2007  rps
 87  219  19*2^916763-1                275975  L177  2007  rps
 88  220  737*2^906168-1               272787  L191  2006  
 89  223  15*2^902474-1                271673   L52  2006  
 90  224  309817*2^901173-1            271286   L64  2004  
 91  225  101*2^900358-1               271037  L183  2006  rps
 92  227  19581121*2^893547-1          268992   p49  2004  
 93  229  2995125705*2^891645-1        268422  L145  2006  rps
 94  233  5077*2^881829-1              265461  L251  2007  rps
 95  238  69*2^867653-1                261192  L138  2006  rps
 96  239  170591*2^866870-1            260960   L47  2004  
 97  240  3234846615*2^865933-1        260682  p113  2007  
 98  241  93997*2^864401-1             260216   L49  2004  
 99  242  19581121*2^862127-1          259534   p49  2003  
100  243  2013289*2^859433-1           258722  L466  2007  
-------------------------------------------------------------------------
26 of them found by RPS.
33 found in 2007.

Happy New Year!
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Old 2008-01-01, 03:43   #2
Kosmaj
 
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Nov 2003

2×1,811 Posts
Default k*2^n-1 primes found in 2007

Here is the list of 100 largest primes of form k*2^n-1, k>=3 found in 2007. Based on the Top-5000 list maintained by prof. Caldwell.

Ranking:
r1, rank among k*2^n-1, k>=3
r2, rank among all known primes

Code:
---------------------------------------------------------------
  r1   r2    description                digits   who  comment
---------------------------------------------------------------
   1   13  938237*2^3752950-1          1129757  L521  Woodall
   2   15  3*2^3136255-1                944108  L256  
   3   22  342673*2^2639439-1           794556   L53  
   4   26  737*2^2382804-1              717299  L191  
   5   27  1183953*2^2367907-1          712818  L447  Woodall
   6   40  251749*2^2013995-1           606279  L436  Woodall
   7   42  137137*2^1993201-1           600019  L321  
   8   48  137*2^1849238-1              556679  L321  
   9   54  253*2^1722623-1              518564  L145  rps
  10   58  469949*2^1649228-1           496473  L160  
  11   80  1467763*2^1467763-1          441847  L381  Woodall
  12   95  15*2^1344313-1               404680  L139  rps
  13  112  1268979*2^1268979-1          382007  L201  Woodall
  14  116  26869*2^1257787-1            378637  L466  
  15  139  617*2^1175468-1              353854  L426  rps
  16  154  99*2^1106989-1               333239  L486  rps
  17  166  864316301*2^1055106-1        317628  L426  rps
  18  169  151515*2^1043018-1           313985  L426  rps
  19  173  85*2^1034069-1               311288  L323  rps
  20  178  6119*2^1011416-1             304471  L251  rps
  21  179  9*2^1010277-1                304125   L80  
  22  190  1515*2^996848-1              300085  L200  rps
  23  197  137137*2^978229-1            294482  L321  
  24  198  69*2^978209-1                294473  L260  rps
  25  204  111*2^959671-1               288892  L282  rps
  26  206  1515*2^955219-1              287553  L200  rps
  27  209  12345*2^948054-1             285397  L200  rps
  28  213  246419198025*2^935249-1      281550  L106  
  29  217  125*2^918494-1               276497  L384  rps
  30  219  19*2^916763-1                275975  L177  rps
  31  233  5077*2^881829-1              265461  L251  rps 
  32  240  3234846615*2^865933-1        260682  p113  
  33  243  2013289*2^859433-1           258722  L466  
  34  244  1486245*2^859433-1           258722  L466  
  35  245  1283911*2^859433-1           258722  L466  
  36  251  83*2^851092-1                256207   L80  
  37  252  261*2^850383-1               255994  L478  rps
  38  255  51*2^845494-1                254521   L80  
  39  257  201*2^840735-1               253089  L282  rps
  40  258  57*2^839446-1                252701   L80  
  41  259  35*2^839082-1                252591  L325  rps
  42  263  117*2^834916-1               251337  L261  rps
  43  265  51*2^832630-1                250649   L80  
  44  266  291*2^832410-1               250583  L261  rps
  45  267  237*2^832053-1               250476  L261  rps
  46  271  173*2^828808-1               249499  L145  rps
  47  273  261*2^827599-1               249135  L261  rps
  48  275  197*2^825188-1               248409  L282  rps
  49  277  181*2^823853-1               248007  L138  rps
  50  282  45*2^818648-1                246440  L282  rps
  51  283  75*2^814857-1                245299   L80  
  52  284  105*2^814850-1               245297  L384  rps
  53  287  291*2^810347-1               243942  L421  rps
  54  290  35*2^805222-1                242398  L142  rps
  55  292  261*2^802123-1               241466  L261  rps
  56  293  105*2^801978-1               241422  L384  rps
  57  308  201*2^799611-1               240710  L282  rps
  58  311  3645*2^792240-1              238492  L261  rps
  59  312  111*2^791502-1               238268  L282  rps
  60  318  285*2^780300-1               234897  L425  rps
  61  320  246419198025*2^778905-1      234486  L106  
  62  324  7003141*2^777777-1           234142   L81  
  63  325  6982195*2^777777-1           234142   L81  
  64  326  6870877*2^777777-1           234142   L81  
  65  327  6655117*2^777777-1           234142   L81  
  66  328  5901565*2^777777-1           234141   L81  
  67  338  201*2^775453-1               233437  L282  rps
  68  339  22183*2^773447-1             232836  L251  rps
  69  340  31*2^773227-1                232767  L330  rps
  70  341  33*2^773030-1                232707  L488  rps
  71  347  213*2^760942-1               229069  L261  rps
  72  348  51127*2^759513-1             228641   L83  
  73  349  246419198025*2^757961-1      228181  L106  
  74  350  1391281*2^756839-1           227838  L466  
  75  351  1334079*2^756839-1           227838  L466  
  76  352  1081255*2^756839-1           227838  L466  
  77  353  755061*2^756839-1            227838  L466  
  78  357  736320585*2^753905-1         226957  L200  rps
  79  358  246419198025*2^752612-1      226571  L106  
  80  368  273*2^742930-1               223647  L323  rps
  81  369  151515*2^742445-1            223504  L200  rps
  82  371  81*2^741917-1                223342  L268  rps
  83  379  237*2^729654-1               219651  L261  rps
  84  384  137137*2^725437-1            218384  L321  
  85  394  91*2^711335-1                214136  L323  rps
  86  396  213*2^709727-1               213652  L261  rps
  87  399  57*2^707245-1                212904  L384  rps
  88  402  151515*2^705873-1            212495  L200  rps
  89  404  267*2^705028-1               212238  L260  rps
  90  406  7331*2^704842-1              212183  L251  rps
  91  416  24067*2^700073-1             210748  L251  rps
  92  417  6215657*2^700000-1           210728   L81  
  93  418  4786305*2^700000-1           210728   L81  
  94  419  4649865*2^700000-1           210728   L81  
  95  422  2758665*2^700000-1           210728   L81  
  96  424  2500883*2^700000-1           210728   L81  
  97  434  117*2^697458-1               209958  L261  rps
  98  436  6794935*2^696969-1           209816   L81  
  99  437  6145851*2^696969-1           209816   L81  
 100  438  4549431*2^696969-1           209816   L81  
---------------------------------------------------------------
54 of them were found by RPS!

The lists at the end of 2006 can be found here.
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