k*2^n-1 primes in 2004

Kosmaj · 2005-01-01, 06:56

Usting the Top-5000 data-base of largest primes I compiled the following list of 100 largest primes k*2^n-1, k>=3 at the end of 2004.

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

Code:

 r1   r2           prime           digits  who  when comment 
  1   18     2232007*2^1490605-1   448724   L4  2003   
  2   20      192089*2^1395688-1   420150  L49  2004   
  3   33      138847*2^1283793-1   386466   L2  2003   
  4   38    80857169*2^1251076-1   376620  L10  2004   
  5   42           3*2^1232255-1   370947  L30  2004   
  6   45           3*2^1201046-1   361552  L77  2004   
  7   46      502541*2^1199930-1   361221  L93  2004   
  8   49       71009*2^1185112-1   356760  L47  2004   
  9   52      152713*2^1154707-1   347607  g23  2004   
 10   54      350107*2^1144101-1   344415  L35  2004   
 11   55   209826493*2^1140855-1   343440  L10  2004   
 12   56      500621*2^1138518-1   342734  L73  2004   
 13   57      504613*2^1136459-1   342114  L84  2004   
 14   60      412717*2^1084409-1   326446  L76  2004   
 15   61      150847*2^1076441-1   324047  L73  2004   
 16   62   209826493*2^1071303-1   322503  L10  2004   
 17   64         121*2^1039965-1   313063  L65  2004   
 18   71           3*2^ 992700-1   298833  L59  2004   
 19   72         121*2^ 990219-1   298088  L66  2004   
 20   75   243163663*2^ 919087-1   276682  L10  2004   
 21   78      309817*2^ 901173-1   271286  L64  2004   
 22   79    19581121*2^ 893547-1   268992  p49  2004   
 23   80      170591*2^ 866870-1   260960  L47  2004   
 24   81       93997*2^ 864401-1   260216  L49  2004   
 25   82    19581121*2^ 862127-1   259534  p49  2003   
 26   91         659*2^ 800516-1   240983  g59  2004   
 27  102      460139*2^ 779536-1   234670  L47  2004   
 28  104      246299*2^ 752600-1   226561  L42  2004   
 29  105          11*2^ 743322-1   223764  L10  2004   
 30  106    19581121*2^ 735431-1   221395  p49  2004   
 31  108      212893*2^ 730387-1   219874  g163 2003   
 32  110           3*2^ 727699-1   219060  L41  2004   
 33  111      220033*2^ 719731-1   216666  g163 2004   
 34  117           3*2^ 702038-1   211335  L30  2003   
 35  125      204223*2^ 696891-1   209791  g163 2003   
 36  127          11*2^ 696438-1   209650  L10  2004   
 37  136      261221*2^ 689422-1   207543  L35  2003   
 38  146         243*2^ 670891-1   201961  p48  2004   
 39  148      667071*2^ 667071-1   200815  g55  2000 Woodall 
 40  162      215503*2^ 649891-1   195643  g163 2003   
 41  163    19581121*2^ 645943-1   194456  p49  2003   
 42  167          29*2^ 644044-1   193879  L10  2004   
 43  172    19581121*2^ 637021-1   191770  p49  2003   
 44  175      109897*2^ 630221-1   189721  g163 2003   
 45  179      126667*2^ 626497-1   188600  g23  2003   
 46  183      279703*2^ 616235-1   185511  L53  2004   
 47  184      103259*2^ 615076-1   185162  g163 2002   
 48  185      222997*2^ 613153-1   184583  g163 2001   
 49  187      357491*2^ 609338-1   183435  g302 2003   
 50  188          77*2^ 607920-1   183005  L56  2004   
 51  189          17*2^ 601158-1   180968  g267 2004   
 52  193   315940139*2^ 595620-1   179308  L10  2004   
 53  196           3*2^ 584995-1   176102  L24  2003   
 54  197        1003*2^ 584103-1   175836  L51  2004   
 55  201       89707*2^ 578313-1   174095  g173 2003   
 56  203       98939*2^ 575144-1   173141  g163 2001   
 57  212      458743*2^ 547791-1   164908  g163 2003   
 58  214         121*2^ 541621-1   163047  L65  2004   
 59  216          21*2^ 538657-1   162154  L56  2004   
 60  217        1337*2^ 533416-1   160578  L51  2004   
 61  224  3234846615*2^ 524946-1   158035  p113 2004   
 62  231       43541*2^ 507098-1   152657  g23  2000   
 63  234           9*2^ 503893-1   151688  L38  2004   
 64  239      144643*2^ 498079-1   149942  g173 2000   
 65  240      465869*2^ 497596-1   149797  g302 2003   
 66  241          23*2^ 496422-1   149440  L40  2004   
 67  243         121*2^ 494317-1   148807  L66  2004   
 68  248           9*2^ 484975-1   145993  L38  2004   
 69  250        1103*2^ 483326-1   145499  L10  2004   
 70  252        1003*2^ 482655-1   145297  L51  2004   
 71  257   276278983*2^ 473423-1   142523  L10  2004
 72  258         105*2^ 472430-1   142218  L38  2004 
 73  261      401617*2^ 470149-1   141535  g59  2002   
 74  263          51*2^ 468417-1   141010  L38  2004   
 75  265          69*2^ 464843-1   139934  L38  2004   
 76  266  3234846615*2^ 464595-1   139867  p113 2004   
 77  267         113*2^ 464386-1   139797  L10  2004   
 78  273          23*2^ 458362-1   137983  L50  2004   
 79  274      201193*2^ 457615-1   137762  g76  2003   
 80  275          15*2^ 454681-1   136874  L52  2004   
 81  276  3234846615*2^ 453034-1   136387  p113 2004   
 82  279          47*2^ 450470-1   135607  L38  2004   
 83  281  2995125705*2^ 449154-1   135219  L32  2004   
 84  285          27*2^ 444622-1   133846  L1   2004   
 85  288   265995345*2^ 441571-1   132935  g344 2004   
 86  289          77*2^ 441528-1   132916  L56  2004   
 87  295      600921*2^ 437954-1   131844  g337 2004   
 88  301   265995345*2^ 431957-1   130041  g344 2004   
 89  304      382691*2^ 431722-1   129967  g23  2003   
 90  305    19581121*2^ 430657-1   129648  p49  2002   
 91  306      277153*2^ 429819-1   129394  g230 2002   
 92  307          17*2^ 429318-1   129239  g267 2003   
 93  308      299617*2^ 428917-1   129123  g59  2002   
 94  309       46271*2^ 428210-1   128909  g188 2001   
 95  310   763094475*2^ 426143-1   128291  L27  2004   
 96  311      416413*2^ 424791-1   127881  g59  2003   
 97  318         113*2^ 422866-1   127298  L10  2004   
 98  349      398533*2^ 419107-1   126170  g59  2002   
 99  350  2995125705*2^ 418999-1   126141  L90  2004   
100  353  3234846615*2^ 417480-1   125684  p113 2004

As of 0600 GMT on January 1, 2005.

Kosmaj · 2005-01-01, 07:03

20 largest primes k*2^n-1, k>=3 discovered in 2004.

Code:

rank         prime           digits  who  when
 1      192089*2^1395688-1   420150  L49  2004
 2    80857169*2^1251076-1   376620  L10  2004
 3           3*2^1232255-1   370947  L30  2004
 4           3*2^1201046-1   361552  L77  2004
 5      502541*2^1199930-1   361221  L93  2004
 6       71009*2^1185112-1   356760  L47  2004
 7      152713*2^1154707-1   347607  g23  2004
 8      350107*2^1144101-1   344415  L35  2004
 9   209826493*2^1140855-1   343440  L10  2004
10      500621*2^1138518-1   342734  L73  2004
11      504613*2^1136459-1   342114  L84  2004
12      412717*2^1084409-1   326446  L76  2004
13      150847*2^1076441-1   324047  L73  2004
14   209826493*2^1071303-1   322503  L10  2004
15         121*2^1039965-1   313063  L65  2004
16           3*2^ 992700-1   298833  L59  2004
17         121*2^ 990219-1   298088  L66  2004
18   243163663*2^ 919087-1   276682  L10  2004
19      309817*2^ 901173-1   271286  L64  2004
20    19581121*2^ 893547-1   268992  p49  2004

Kosmaj · 2005-01-01, 07:22

A list of 20 largest primes of this kind as of May 15, 2004 can be found here. It is interesting that only top 4 primes on that list are still among 20 largest of all times (cf. the top post). It testifies to the tremendous speed at which these primes are being discovered.

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2005-01-01, 07:22	#3
Kosmaj Nov 2003 2×1,811 Posts	A list of 20 largest primes of this kind as of May 15, 2004 can be found here. It is interesting that only top 4 primes on that list are still among 20 largest of all times (cf. the top post). It testifies to the tremendous speed at which these primes are being discovered.