Thema: Maximale Lücken (Intervallen) von Primzahlenzwillingen
Main index: http://www.fermatquotient.com/

Siehe auch unter:
http://www.research.att.com/~njas/sequences/?q=13%2C181%2C2521&language=english&go=Search
 A113274  ,  A113275  bzw.  A036061

Beginn Zahl: 3
Rekord-Lücke, 1. Primzahl, letzte Primzahl der gefundenen Lücke, relativ
 2, 3, 7, 0.470061
   Merit: 1.019 = 2*T/(ln 5)^2 ; T = 1.32032363169...
 6, 5, 13, 0.518477
   Merit: 2.092 = 6*T/(ln 7)^2
 12, 17, 31, 0.402883
 18, 41, 61, 0.346293
 30, 71, 103, 0.400394
   Merit: 2.152 = 30*T/(ln 73)^2
 36, 311, 349, 0.237151
 72, 347, 421, 0.431368
   Merit: 2.773 = 72*T/(ln 349)^2
 150, 659, 811, 0.659362
   Merit: 4.697 = 150*T/(ln 661)^2
 168, 2381, 2551, 0.459623
 210, 5879, 6091, 0.418974
 282, 13397, 13681, 0.431036
 372, 18539, 18913, 0.514326
   Merit: 5.085 = 372*T/(ln 18541)^2
 498, 24419, 24919, 0.633779
   Merit: 6.442 = 498*T/(ln 24421)^2
 630, 62297, 62929, 0.616544
   Merit: 6.825 = 630*T/(ln 62299)^2
 924, 187907, 188833, 0.680412
   Merit: 8.273 = 924*T/(ln 187909)^2
 930, 687521, 688453, 0.505536
 1008, 688451, 689461, 0.547757
 1452, 850349, 851803, 0.752942
   Merit: 10.284 = 1452*T/(ln 850351)^2
 1512, 2868959, 2870473, 0.607156
 1530, 4869911, 4871443, 0.553226
 1722, 9923987, 9925711, 0.543720
 1902, 14656517, 14658421, 0.558982
 2190, 17382479, 17384671, 0.624068
   Merit: 10.404 = 2190*T/(ln 17382481)^2
 2256, 30752231, 30754489, 0.581153
 2832, 32822369, 32825203, 0.721324
   Merit: 12.484 = 2832*T/(ln 32822371)^2
 2868, 96894041, 96896911, 0.608939
 3012, 136283429, 136286443, 0.605206
 3102, 234966929, 234970033, 0.571928
 3180, 248641037, 248644219, 0.581177
 3480, 255949949, 255953431, 0.633154
 3804, 390817727, 390821533, 0.648626
   Merit: 12.832 = 3804*T/(ln 390817729)^2
 4770, 698542487, 698547259, 0.745721
   Merit: 15.186 = 4770*T/(ln 698542489)^2
 5292, 2466641069, 2466646363, 0.690819
 6030, 4289385521, 4289391553, 0.729706
   Merit: 16.184 = 6030*T/(ln 4289385523)^2
 6282, 19181736269, 19181742553, 0.624865
 6474, 24215097497, 24215103973, 0.625318
 6552, 24857578817, 24857585371, 0.630778
 6648, 40253418059, 40253424709, 0.602860
 7050, 42441715487, 42441722539, 0.635175
 7980, 43725662621, 43725670603, 0.716343
   Merit: 17.551 = 7980*T/(ln 43725662623)^2
 8040, 65095731749, 65095739791, 0.687677
 8994, 134037421667, 134037430663, 0.706034
   Merit: 18.090 = 8994*T/(ln 134037421669)^2
 9312, 198311685749, 198311695063, 0.698468
   Merit: 18.169 = 9312*T/(ln 198311685751)^2
 9318, 223093059731, 223093069051, 0.689513
 10200, 353503437239, 353503447441, 0.716257
   Merit: 19.046 = 10200*T/(ln 353503437241)^2
 10338, 484797803249, 484797813589, 0.700682
 10668, 638432376191, 638432386861, 0.701303
   Merit: 19.063 = 10668*T/(ln 638432376193)^2
 10710, 784468515221, 784468525933, 0.688297
 11388, 794623899269, 794623910659, 0.730840
   Merit: 20.026 = 11388*T/(ln 794623899271)^2
 11982, 1246446371789, 1246446383773, 0.732272
   Merit: 20.395 = 11982*T/(ln 1246446371791)^2
 12138, 1344856591289, 1344856603429, 0.735767
   Merit: 20.548 = 12138*T/(ln 1344856591291)^2
 12288, 1496875686461, 1496875698751, 0.736356
   Merit: 20.643 = 12288*T/(ln 1496875686463)^2
 12630, 2156652267611, 2156652280243, 0.728028
   Merit: 20.676 = 12630*T/(ln 2156652267613)^2
 13050, 2435613754109, 2435613767161, 0.742654
   Merit: 21.181 = 13050*T/(ln 2435613754111)^2
 14262, 4491437003327, 4491437017591, 0.761547
   Merit: 22.186 = 14262*T/(ln 4491437003329)^2
 14436, 13104143169251, 13104143183689, 0.691729
 14952, 14437327538267, 14437327553221, 0.709604
 15396, 18306891187511, 18306891202909, 0.713763
 15720, 18853633225211, 18853633240933, 0.726681
   Merit: 22.213 = 15720*T/(ln 18853633225213)^2
 16362, 23275487664899, 23275487681263, 0.74093
   Merit: 22.805 = 16362*T/(ln 23275487664901)^2
 16422, 23634280586867, 23634280603291, 0.742540
   Merit: 22.866 = 16422*T/(ln 23634280586869)^2
 16590, 38533601831027, 38533601847619, 0.715518
 16896, 43697538391391, 43697538408289, 0.719997
 17082, 56484333976919, 56484333994003, 0.710365
 18384, 74668675816277, 74668675834663, 0.744645
   Merit: 23.787 = 18384*T/(ln 74668675816279)^2
 19746, 116741875898981, 116741875918729, 0.767162
   Merit: 24.849 = 19746*T/(ln 116741875898983)^2
 19992, 136391104728629, 136391104748623, 0.765635
   Merit: 24.919 = 19992*T/(ln 136391104728631)^2
 20532, 221346439666109, 221346439686643, 0.752240
 21930, 353971046703347, 353971046725279, 0.770150
   Merit: 25.800 = 21930*T/(ln 353971046703349)^2
 22548, 450811253543219, 450811253565769, 0.774949
   Merit: 26.148 = 22548*T/(ln 450811253543221)^2
 23358, 742914612256169, 742914612279529, 0.768164
   Merit: 26.303 = 23358*T/(ln 742914612256171)^2
 23382, 1121784847637957, 1121784847661341, 0.741845
 25230, 1149418981410179, 1149418981435411, 0.798793
   Merit: 27.701 = 25230*T/(ln 1149418981410181)^2
Durchsucht bis 1.28E+15

relativ = Rekordlücke * T / ln[Wurzel((letzte Primzahl - 2)*(letzte Primzahl))]^3
Praktisch:  relativ = Rekordlücke * T / ln(letzte Primzahl - 1)^3
T = 1.32032363169...

Ende der Suche für eine längere Zeit

10.01.2008  Richard Fischer