Thema: Maximale Luecken (Intervallen) von Primzahlen-Zwillingen und -Cousins Topic: Record gaps of neighboring twin and cousin prime numbers Main index: http://www.fermatquotient.com/ Siehe auch unter / See too: http://oeis.org/ A113274 , A113275 , A036061 https://github.com/danaj/Math-Prime-Util-GMP/blob/master/t/12-nextprime.t Primzahlen-Zwillinge ±1 ; Twin prime numbers ±1 relativ = Rekordluecke * T / {ln(letzte Primzahl - 1)-ln[ln(letzte Primzahl - 1)]/3}^3 relative = (Record gap) * T / {ln(last prime number - 1)-ln[ln(last prime number - 1)]/3}^3 T = 1.32032363169... = Twin Prime Constant Rekord-Luecke, 1. Primzahl, letzte Primzahl der gefundenen Luecke, relativ Record gap, 1. prime number, last prime number of the found gap, relative 2, 3, 7, 0.64789 Merit: 1.019 = 2*T/(ln 5)^2 6, 5, 13, 0.76308 Merit: 2.092 = 6*T/(ln 7)^2 12, 17, 31, 0.59085 18, 41, 61, 0.49913 30, 71, 103, 0.56866 Merit: 2.152 = 30*T/(ln 73)^2 36, 311, 349, 0.32600 72, 347, 421, 0.59024 Merit: 2.773 = 72*T/(ln 349)^2 150, 659, 811, 0.88854 Merit: 4.697 = 150*T/(ln 661)^2 168, 2381, 2551, 0.60499 210, 5879, 6091, 0.54302 282, 13397, 13681, 0.55153 372, 18539, 18913, 0.65498 Merit: 5.085 = 372*T/(ln 18541)^2 498, 24419, 24919, 0.80396 Merit: 6.442 = 498*T/(ln 24421)^2 630, 62297, 62929, 0.77265 Merit: 6.825 = 630*T/(ln 62299)^2 924, 187907, 188833, 0.84188 Merit: 8.273 = 924*T/(ln 187909)^2 930, 687521, 688453, 0.61735 1008, 688451, 689461, 0.66890 1452, 850349, 851803, 0.91764 Merit: 10.284 = 1452*T/(ln 850351)^2 1512, 2868959, 2870473, 0.73219 1530, 4869911, 4871443, 0.66435 1722, 9923987, 9925711, 0.64945 1902, 14656517, 14658421, 0.66582 2190, 17382479, 17384671, 0.74246 Merit: 10.404 = 2190*T/(ln 17382481)^2 2256, 30752231, 30754489, 0.68875 2832, 32822369, 32825203, 0.85451 Merit: 12.484 = 2832*T/(ln 32822371)^2 2868, 96894041, 96896911, 0.71651 3012, 136283429, 136286443, 0.71069 3102, 234966929, 234970033, 0.66955 3180, 248641037, 248644219, 0.68015 3480, 255949949, 255953431, 0.74086 3804, 390817727, 390821533, 0.75722 Merit: 12.832 = 3804*T/(ln 390817729)^2 4770, 698542487, 698547259, 0.86794 Merit: 15.186 = 4770*T/(ln 698542489)^2 5292, 2466641069, 2466646363, 0.79911 6030, 4289385521, 4289391553, 0.84196 Merit: 16.184 = 6030*T/(ln 4289385523)^2 6282, 19181736269, 19181742553, 0.71641 6474, 24215097497, 24215103973, 0.71626 6552, 24857578817, 24857585371, 0.72244 6648, 40253418059, 40253424709, 0.68917 7050, 42441715487, 42441722539, 0.72596 7980, 43725662621, 43725670603, 0.81864 Merit: 17.551 = 7980*T/(ln 43725662623)^2 8040, 65095731749, 65095739791, 0.78469 8994, 134037421667, 134037430663, 0.80352 Merit: 18.090 = 8994*T/(ln 134037421669)^2 9312, 198311685749, 198311695063, 0.79381 Merit: 18.169 = 9312*T/(ln 198311685751)^2 9318, 223093059731, 223093069051, 0.78331 10200, 353503437239, 353503447441, 0.81242 Merit: 19.046 = 10200*T/(ln 353503437241)^2 10338, 484797803249, 484797813589, 0.79392 10668, 638432376191, 638432386861, 0.79391 Merit: 19.063 = 10668*T/(ln 638432376193)^2 10710, 784468515221, 784468525933, 0.77867 11388, 794623899269, 794623910659, 0.82676 Merit: 20.026 = 11388*T/(ln 794623899271)^2 11982, 1246446371789, 1246446383773, 0.82720 Merit: 20.395 = 11982*T/(ln 1246446371791)^2 12138, 1344856591289, 1344856603429, 0.83095 Merit: 20.548 = 12138*T/(ln 1344856591291)^2 12288, 1496875686461, 1496875698751, 0.83134 Merit: 20.643 = 12288*T/(ln 1496875686463)^2 12630, 2156652267611, 2156652280243, 0.82102 Merit: 20.676 = 12630*T/(ln 2156652267613)^2 13050, 2435613754109, 2435613767161, 0.83721 Merit: 21.181 = 13050*T/(ln 2435613754111)^2 14262, 4491437003327, 4491437017591, 0.85695 Merit: 22.186 = 14262*T/(ln 4491437003329)^2 14436, 13104143169251, 13104143183689, 0.77604 14952, 14437327538267, 14437327553221, 0.79588 15396, 18306891187511, 18306891202909, 0.80003 15720, 18853633225211, 18853633240933, 0.81445 Merit: 22.213 = 15720*T/(ln 18853633225213)^2 16362, 23275487664899, 23275487681263, 0.82995 Merit: 22.805 = 16362*T/(ln 23275487664901)^2 16422, 23634280586867, 23634280603291, 0.83172 Merit: 22.866 = 16422*T/(ln 23634280586869)^2 16590, 38533601831027, 38533601847619, 0.80042 16896, 43697538391391, 43697538408289, 0.80517 17082, 56484333976919, 56484333994003, 0.79388 18384, 74668675816277, 74668675834663, 0.83160 Merit: 23.787 = 18384*T/(ln 74668675816279)^2 19746, 116741875898981, 116741875918729, 0.85580 Merit: 24.849 = 19746*T/(ln 116741875898983)^2 19992, 136391104728629, 136391104748623, 0.85377 Merit: 24.919 = 19992*T/(ln 136391104728631)^2 20532, 221346439666109, 221346439686643, 0.83786 21930, 353971046703347, 353971046725279, 0.85687 Merit: 25.800 = 21930*T/(ln 353971046703349)^2 22548, 450811253543219, 450811253565769, 0.86173 Merit: 26.148 = 22548*T/(ln 450811253543221)^2 23358, 742914612256169, 742914612279529, 0.85321 Merit: 26.303 = 23358*T/(ln 742914612256171)^2 23382, 1121784847637957, 1121784847661341, 0.82323 25230, 1149418981410179, 1149418981435411, 0.88638 Merit: 27.701 = 25230*T/(ln 1149418981410181)^2 26268, 2543288406389231, 2543288406415501, 0.86076 28842, 2797282815481499, 2797282815510343, 0.93735 * Merit: 30.102 = 28842*T/(ln 2797282815481501)^2 31302, 12914226879316517, 12914226879347821, 0.89380 31482, 16155559543324757, 16155559543356241, 0.88246 31512, 37338553629118097, 37338553629149611, 0.82508 31920, 37962553054417547, 37962553054449469, 0.83464 33042, 38617975949216087, 38617975949249131, 0.86279 34692, 52000545890760149, 52000545890794843, 0.88454 Merit: 30.918 = 34692*T/(ln 52000545890760151)^2 35640, 70478530884377381, 70478530884413023, 0.88702 Merit: 31.267 = 35640*T/(ln 70478530884377383)^2 Primzahlen-Cousins ±2 ; Cousin prime numbers ±2 relativ = Rekordluecke * T / {ln(letzte Primzahl - 2)-ln[ln(letzte Primzahl - 2)]/3}^3 relative = (Record gap) * T / {ln(last prime number - 2)-ln[ln(last prime number - 2)]/3}^3 T = 1.32032363169... = Twin Prime Constant Rekord-Luecke, 1. Primzahl, letzte Primzahl der gefundenen Luecke, relativ Record gap, 1. prime number, last prime number of the found gap, relative 4, 3, 11, 0.72915 6, 7, 17, 0.59062 18, 19, 41, 0.70476 24, 43, 71, 0.59943 36, 127, 167, 0.50047 48, 229, 281, 0.49060 114, 499, 617, 0.77075 120, 1093, 1217, 0.59072 126, 4003, 4133, 0.37603 294, 4153, 4451, 0.85325 354, 10729, 11087, 0.74270 396, 37567, 37967, 0.56251 426, 80173, 80603, 0.48739 462, 135727, 136193, 0.45848 480, 146059, 146543, 0.46721 756, 174763, 175523, 0.70196 810, 250027, 250841, 0.68650 876, 511627, 512507, 0.62331 960, 706837, 707801, 0.63317 990, 963223, 964217, 0.60824 1038, 979549, 980591, 0.63530 1074, 1598539, 1599617, 0.58950 1110, 1640263, 1641377, 0.60583 1116, 2011903, 2013023, 0.58276 1182, 2043907, 2045093, 0.61513 1434, 2535469, 2536907, 0.71274 1470, 4644667, 4646141, 0.64446 1500, 5603929, 5605433, 0.63314 1926, 6549247, 6551177, 0.78803 1938, 13043119, 13045061, 0.69358 1986, 20441467, 20443457, 0.65331 2166, 23122387, 23124557, 0.69652 2310, 26540053, 26542367, 0.72433 2436, 28801477, 28803917, 0.75257 2670, 31871713, 31874387, 0.809900 3066, 100586173, 100589243, 0.76115 3162, 217710877, 217714043, 0.69095 3654, 279673573, 279677231, 0.76694 4158, 430574359, 430578521, 0.81523 4284, 968193433, 968197721, 0.74197 4326, 1098972643, 1098976973, 0.73518 4854, 1533615103, 1533619961, 0.78526 5052, 3294327607, 3294332663, 0.73207 6234, 4540542679, 4540548917, 0.86356 6390, 8761474699, 8761481093, 0.80877 6660, 14889114259, 14889120923, 0.78524 7404, 17322600289, 17322607697, 0.85572 7686, 17353381537, 17353389227, 0.88811 8184, 63863620279, 63863628467, 0.80065 8970, 144324102019, 144324110993, 0.79427 9042, 157403337697, 157403346743, 0.79235 9366, 158054409577, 158054418947, 0.82033 9516, 166595684263, 166595693783, 0.82823 10434, 398578013083, 398578023521, 0.81958 10590, 612421438873, 612421449467, 0.79184 11712, 618435943717, 618435955433, 0.87476 12396, 750505202893, 750505215293, 0.90576 * 11994, 1184535811579, 1184535823577, 0.83272 12054, 1338289570729, 1338289582787, 0.82565 12600, 2756648330833, 2756648343437, 0.79761 12606, 2913465736873, 2913465749483, 0.79325 13056, 4187027825023, 4187027838083, 0.79035 13530, 4223478812677, 4223478826211, 0.81829 13986, 6453899004463, 6453899018453, 0.80892 14334, 7940912915713, 7940912930051, 0.81133 14850, 8024613978253, 8024613993107, 0.83962 15804, 10200314199739, 10200314215547, 0.87168 16272, 17519182119037, 17519182135313, 0.84932 16890, 34002720255079, 34002720271973, 0.82502 17430, 34863373958107, 34863373975541, 0.84929 18576, 60048237161053, 60048237179633, 0.85819 18612, 63172947710707, 63172947729323, 0.85563 19608, 100943601658429, 100943601678041, 0.86168 10.02.2025 Richard Fischer