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Old 2010-01-01, 08:48   #1
Kosmaj
 
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Nov 2003

E2616 Posts
Default k*2^n-1 Primes in 2009

Here is the list of 100 largest primes of form k*2^n-1, k>=3 discovered in 2009. Based on the Top-5000 list maintained by prof. Caldwell.

Ranking:
r1, rank among k*2^n-1, k>=3 found in 2009
r2, rank among all known primes

The list of largest primes found in 2008 can be found here.

Happy New Year!

Code:
----------------------------------------------------------
 r1   r2        description         digits   who   date
----------------------------------------------------------
  1   25  5*2^3569154-1            1074424  L503  Jan 2009 
  2   50  127*2^2346377-1           706332  L282  Jul 2009 
  3   77  27*2^1902689-1            572768 L1153  Dec 2009 
  4  110  99*2^1591984-1            479237  L282  Mar 2009 
  5  114  311*2^1581686-1           476138  L623  Jun 2009 
  6  133  99*2^1461496-1            439957  L282  Mar 2009 
  7  139  9*2^1419855-1             427420  L323  Nov 2009 
  8  143  105*2^1407665-1           423752  L384  Dec 2009 
  9  158  107*2^1362654-1           410202  L621  Jul 2009 
 10  160  299*2^1355004-1           407900  L426  Oct 2009 
 11  177  19581121*2^1303821-1      392497   p49  Jul 2009 
 12  217  105*2^1193072-1           359153  L384  Nov 2009 
 13  222  21*2^1182083-1            355844  L323  Aug 2009 
 14  245  842711*2^1126138-1        339008  L251  Feb 2009 
 15  263  103*2^1077739-1           324434  L621  Jun 2009 
 16  275  41*2^1059562-1            318962  L282  Mar 2009 
 17  279  12345*2^1047788-1         315420  L426  May 2009 
 18  281  105*2^1043063-1           313996  L384  Jun 2009 
 19  298  41*2^1018778-1            306685  L282  Sep 2009 
 20  309  8009271*2^1000005-1       301039  g396  Mar 2009 
 21  316  335*2^997912-1            300404  L769  Oct 2009 
 22  320  53355*2^996559-1          299999  L466  Oct 2009 
 23  325  9405*2^995003-1           299530  L644  Dec 2009 
 24  326  9945*2^994111-1           299262  L644  Oct 2009 
 25  327  371*2^993238-1            298998  L644  Jul 2009 
 26  330  19861029*2^991533-1       298489  L895  Dec 2009 
 27  331  9615*2^991347-1           298430  L644  Jun 2009 
 28  335  351*2^985817-1            296764  L536  Sep 2009 
 29  336  189*2^984683-1            296422  L384  Aug 2009 
 30  337  103*2^984667-1            296417  L621  May 2009 
 31  338  395*2^983160-1            295964  L644  Jan 2009 
 32  340  333*2^982086-1            295640  L536  Aug 2009 
 33  346  103*2^977951-1            294395  L621  May 2009 
 34  349  375*2^976533-1            293969  L644  Nov 2009 
 35  353  3003*2^973751-1           293132  L615  Jul 2009 
 36  358  123*2^968927-1            291679  L384  Aug 2009 
 37  363  3001*2^966755-1           291026  L615  Jun 2009 
 38  364  19861029*2^966404-1       290924  L895  Nov 2009 
 39  366  195*2^963608-1            290078  L323  Nov 2009 
 40  374  123*2^958050-1            288404  L384  Sep 2009 
 41  375  1845*2^955940-1           287770  L251  Feb 2009 
 42  379  309*2^954323-1            287283  L548  Jan 2009 
 43  385  327*2^949109-1            285713  L536  Jul 2009 
 44  386  1845*2^948584-1           285556  L251  Feb 2009 
 45  390  1545*2^946280-1           284862  L251  Jan 2009 
 46  393  245*2^943088-1            283901  L282  Dec 2009 
 47  396  321*2^942046-1            283587  L536  Jul 2009 
 48  397  2943*2^940906-1           283245  L862  Aug 2009 
 49  399  123*2^939098-1            282699  L257  Aug 2009 
 50  400  277*2^937325-1            282166  L323  Jun 2009 
 51  401  375*2^936717-1            281983  L644  Oct 2009 
 52  406  3039469*2^933473-1        281010  L466  Aug 2009 
 53  409  3039469*2^928643-1        279556  L466  Aug 2009 
 54  411  465*2^928115-1            279394  L198  Feb 2009 
 55  420  1575*2^920488-1           277098  L860  Oct 2009 
 56  431  195*2^915929-1            275725  L323  May 2009 
 57  438  207*2^912512-1            274696  L330  May 2009 
 58  442  3039469*2^908463-1        273482  L466  Jun 2009 
 59  443  251*2^907478-1            273181  L421  Jan 2009 
 60  454  3005*2^902580-1           271708  L615  Jul 2009 
 61  458  3045*2^902181-1           271588  L615  Jul 2009 
 62  462  297*2^899234-1            270699  L421  Jun 2009 
 63  463  371*2^898690-1            270536  L644  Jun 2009 
 64  467  153*2^894504-1            269275  L384  Jun 2009 
 65  470  345*2^894064-1            269143  L536  Jun 2009 
 66  472  333*2^893871-1            269085  L536  Jun 2009 
 67  476  189*2^891876-1            268484  L621  Jun 2009 
 68  482  189*2^888200-1            267378  L323  Jun 2009 
 69  488  3003*2^882106-1           265544  L615  Jul 2009 
 70  495  141*2^878798-1            264547  L282  Feb 2009 
 71  496  3135*2^878081-1           264333  L615  Jul 2009 
 72  505  108045*2^875337-1         263508  L466  Mar 2009 
 73  507  108045*2^871024-1         262210  L466  Mar 2009 
 74  509  2953*2^870435-1           262031  L862  Jun 2009 
 75  511  327*2^869829-1            261848  L536  May 2009 
 76  513  405405*2^868467-1         261441  L466  Jul 2009 
 77  519  1815*2^863743-1           260016  L251  Feb 2009 
 78  520  391*2^863459-1            259930  L644  Jul 2009 
 79  527  3793717*2^859433-1        258722  L466  Apr 2009 
 80  528  3512185*2^859433-1        258722  L466  Jan 2009 
 81  537  405405*2^857986-1         258286  L466  Jul 2009 
 82  544  2951*2^852818-1           256728  L862  May 2009 
 83  550  377*2^850160-1            255927  L644  Jun 2009 
 84  553  315*2^846610-1            254858  L585  May 2009 
 85  555  1575*2^845854-1           254631  L251  Sep 2009 
 86  558  147687*2^843689-1         253981  L550  Jan 2009 
 87  560  325*2^842787-1            253707  L848  Jul 2009 
 88  561  211*2^842347-1            253575  L915  Aug 2009 
 89  577  367*2^834573-1            251235  L644  Feb 2009 
 90  580  333*2^832611-1            250644  L536  May 2009 
 91  585  111546435*2^831835-1      250416  L466  Dec 2009 
 92  597  465*2^825730-1            248573  L198  Feb 2009 
 93  598  351*2^825586-1            248529  L701  Aug 2009 
 94  634  325*2^809389-1            243653  L848  Jun 2009 
 95  635  3135*2^809190-1           243594  L615  Jul 2009 
 96  644  3997*2^803217-1           241797  L644  Jan 2009 
 97  651  153*2^800567-1            240997  L323  Jan 2009 
 98  687  3003*2^786991-1           236912  L615  Jul 2009 
 99  688  375*2^786387-1            236729  L644  Jun 2009 
100  692  333*2^783927-1            235989  L536  May 2009 
----------------------------------------------------------
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Old 2010-01-01, 10:25   #2
em99010pepe
 
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I got r1=8, 12, 18, 29, 36, 40 and 64. Cool!

Last fiddled with by em99010pepe on 2010-01-01 at 10:25
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Old 2011-01-02, 15:39   #3
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Default k*2^n-1 Primes in 2010

Waiting for k*2^n-1 Primes in 2010...
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Old 2011-01-05, 04:26   #4
Kosmaj
 
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Carlos, here and sorry for the delay this time.
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