| Pattern d: d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42 | ||||||
|
merit = 9931.31564588 ·∫dt / log12 t Gap start | Rank | Gap Size | Gap start | Next Prime 12-tuplet | Merit | Who | When |
| 1 | 380284918609470 | 11 | 380284918609481 | 3.839834 | Norman Luhn | 08 Nov 2022 |
| 2 | 730994620000260 | 2325810733931801 | 3056805353932061 | 1.797107 | Norman Luhn | 08 Nov 2022 |
| 3 | 1156467011129430 | 3843547642594391 | 5000014653723821 | 2.406637 | Norman Luhn | 08 Nov 2022 |
| 4 | 1625376442730040 | 5861268883004651 | 7486645325734691 | 2.950754 | Norman Luhn | 08 Nov 2022 |
| 5 | 1741571240305050 | 9354490866900911 | 11096062107205961 | 2.747902 | Norman Luhn | 08 Nov 2022 |
| 6 | 2668295607837090 | 11096434547374061 | 13764730155211151 | 3.952679 | Norman Luhn | 08 Nov 2022 |
| 7 | 3553919388655020 | 13884748604026031 | 17438667992681051 | 4.886666 | Norman Luhn | 08 Nov 2022 |
| 8 | 5127067548646890 | 52018707666681641 | 57145775215328531 | 4.744677 | Norman Luhn | 08 Nov 2022 |
| 9 | 5616368602424580 | 76924367955394691 | 82540736557819271 | 4.621322 | Norman Luhn | 08 Nov 2022 |
| 10 | 8214050440385790 | 213666617237598641 | 221880667677984431 | 4.977331 | Norman Luhn | 08 Nov 2022 |
| 11 | 10082975445203430 | 710305234161578171 | 720388209606781601 | 4.295675 | Norman Luhn | 08 Nov 2022 |
| 12 | 13803780789903720 | 842150466930838181 | 855954247720741901 | 5.594543 | Norman Luhn | 08 Nov 2022 |
| 13 | 14904048947012610 | 972897069622697951 | 987801118569710561 | 5.793625 | Norman Luhn | 08 Nov 2022 |
| 14 | 16697253112194270 | 1215437797271032451 | 1232135050383226721 | 6.087837 | Norman Luhn | 08 Nov 2022 |
| 15 | 22283330984278980 | 1750596311066427941 | 1772879642050706921 | 7.318202 | Norman Luhn | 08 Nov 2022 |
| 16 | 28322124733767480 | 6015907930528441061 | 6044230055262208541 | 6.578214 | Norman Luhn | 08 Nov 2022 |
| 17 | 29210976284219730 | 6463178617412776991 | 6492389593696996721 | 6.651260 | Norman Luhn | 08 Nov 2022 |
| 18 | 41232205411396230 | 11864234860023131471 | 11905467065434527701 | 7.944788 | Norman Luhn | 08 Nov 2022 |
| 19 | 42815390293559730 | 18456902605404919541 | 18499717995698479271 | 7.317128 | Norman Luhn | 08 Nov 2022 |
| 20 | 43768620900194190 | 31199299677935298641 | 31243068298835492831 | 6.496055 | Norman Luhn | 08 Nov 2022 |
| 21 | 45368816662803480 | 31353462805331853071 | 31398831621994656551 | 6.724647 | Norman Luhn | 08 Nov 2022 |
| 22 | 46115843740155420 | 31806581242063173431 | 31852697085803328851 | 6.809208 | Norman Luhn | 08 Nov 2022 |
| 23 | 46249828837807980 | 32811050444836763831 | 32857300273674571811 | 6.772544 | Norman Luhn | 08 Nov 2022 |
| 24 | 51891894827376450 | 39907888432287161171 | 39959780327114537621 | 7.212546 | Norman Luhn | 08 Nov 2022 |
| 25 | 56205562817358570 | 40948735322273774111 | 41004940885091132681 | 7.758756 | Norman Luhn | 08 Nov 2022 |
| 26 | 58450769687360820 | 46031616939215482691 | 46090067708902843511 | 7.822101 | Norman Luhn | 08 Nov 2022 |
| 27 | 68232666277270110 | 46495107407071818611 | 46563340073349088721 | 9.106702 | Norman Luhn | 08 Nov 2022 |
| 28 | 78121406190493050 | 55246918181602537121 | 55325039587793030171 | 9.961677 | Norman Luhn | 08 Nov 2022 |
| 29 | 89353255172520570 | 73186854355557027971 | 73276207610729548541 | Norman Luhn | 08 Nov 2022 | |
|
| ||||||
| Pattern d: d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42 | ||||||
|
merit = 9931.315645884 ·∫dt / log12 t Gap start | Rank | Gap Size | Gap start | Next Prime 12-tuplet | Merit | Who | When |
| 1 | 26480783759430 | 1418575498567 | 27899359257997 | 0.495041 | Norman Luhn | 08 Nov 2022 |
| 2 | 41614642273050 | 34460918582317 | 76075560855367 | 0.415610 | Norman Luhn | 08 Nov 2022 |
| 3 | 110385055740960 | 76075560855367 | 186460616596327 | 0.799984 | Norman Luhn | 08 Nov 2022 |
| 4 | 258321583103430 | 346117552180627 | 604439135284057 | 1.163194 | Norman Luhn | 08 Nov 2022 |
| 5 | 314397115953690 | 727417501795057 | 1041814617748747 | 1.133561 | Norman Luhn | 08 Nov 2022 |
| 6 | 449011245358830 | 1090754719898917 | 1539765965257747 | 1.410600 | Norman Luhn | 08 Nov 2022 |
| 7 | 1612279735690470 | 1539765965257747 | 3152045700948217 | 4.186116 | Norman Luhn | 08 Nov 2022 |
| 8 | 2279016219020310 | 12448240792011097 | 14727257011031407 | 3.279134 | Norman Luhn | 08 Nov 2022 |
| 9 | 2296661431164870 | 33850998835087507 | 36147660266252377 | 2.442549 | Norman Luhn | 08 Nov 2022 |
| 10 | 3719476464303600 | 41699005945450927 | 45418482409754527 | 3.693222 | Norman Luhn | 08 Nov 2022 |
| 11 | 5206713159317670 | 104398760602501207 | 109605473761818877 | 3.913900 | Norman Luhn | 08 Nov 2022 |
| 12 | 6469229085525360 | 230683996240061437 | 237153225325586797 | 3.836713 | Norman Luhn | 08 Nov 2022 |
| 13 | 6535297809706050 | 329171818692341467 | 335707116502047517 | 3.489538 | Norman Luhn | 08 Nov 2022 |
| 14 | 6883525538109990 | 470229421395357697 | 477112946933467687 | 3.309613 | Norman Luhn | 08 Nov 2022 |
| 15 | 7399719604923030 | 477841999647717547 | 485241719252640577 | 3.540559 | Norman Luhn | 08 Nov 2022 |
| 16 | 12736599614829090 | 597490335533611747 | 610226935148440837 | 5.701904 | Norman Luhn | 08 Nov 2022 |
| 17 | 13280420526939720 | 1006202936672747887 | 1019483357199687607 | 5.113957 | Norman Luhn | 08 Nov 2022 |
| 18 | 14726026197232350 | 1534313413978529257 | 1549039440175761607 | 5.024435 | Norman Luhn | 08 Nov 2022 |
| 19 | 16985783722427520 | 2736923117861757667 | 2753908901584185187 | 4.917753 | Norman Luhn | 08 Nov 2022 |
| 20 | 19324036798015950 | 3196971583799687767 | 3216295620597703717 | 5.354908 | Norman Luhn | 08 Nov 2022 |
| 21 | 30505629576077040 | 4340364707711477287 | 4370870337287554327 | 7.757354 | Norman Luhn | 08 Nov 2022 |
| 22 | 52342627155098280 | 8442259333940076487 | 8494601961095174767 | 11.06806 | Norman Luhn | 08 Nov 2022 |
| 23 | 55732128780007680 | 34535601422849397097 | 34591333551629404777 | 8.050043 | Norman Luhn | 08 Nov 2022 |
| 24 | 56668138219806960 | 43627414062551299207 | 43684082200771106167 | 7.692166 | Norman Luhn | 08 Nov 2022 |
| 25 | 59188048111966620 | 48264394767207128737 | 48323582815319095357 | 7.822049 | Norman Luhn | 08 Nov 2022 |
| 26 | 63363866162947350 | 53573127339112941787 | 53636491205275889137 | 8.146020 | Norman Luhn | 08 Nov 2022 |
| 27 | 66073654250449230 | 63009262874723800477 | 63075336528974249707 | 8.138819 | Norman Luhn | 08 Nov 2022 |
| 28 | 74328817388190750 | 75714542920258196797 | 75788871737646387547 | 8.724458 | Norman Luhn | 08 Nov 2022 |
| 29 | 97811020124788740 | 76574557450058101507 | 76672368470182890247 | Norman Luhn | 08 Nov 2022 | |
|
| ||||||
|
merit = 19862.6312917696 ·∫dt / log12 t Gap start | Rank | Gap Size | Gap start | Next Prime 12-tuplet | Merit | Who | When |
| 1 | 1418575498556 | 11 | 1418575498567 | 1.988290 | Norman Luhn | 18 Jan 2023 |
| 2 | 26480783759430 | 1418575498567 | 27899359257997 | 0.990082 | Norman Luhn | 18 Jan 2023 |
| 3 | 41614642273050 | 34460918582317 | 76075560855367 | 0.831220 | Norman Luhn | 18 Jan 2023 |
| 4 | 110385055740960 | 76075560855367 | 186460616596327 | 1.599969 | Norman Luhn | 18 Jan 2023 |
| 5 | 167275369395476 | 437163765888581 | 604439135284057 | 1.452407 | Norman Luhn | 18 Jan 2023 |
| 6 | 252707529286024 | 727417501795057 | 980125031081081 | 1.843526 | Norman Luhn | 18 Jan 2023 |
| 7 | 294228747907984 | 1539765965257747 | 1833994713165731 | 1.694305 | Norman Luhn | 18 Jan 2023 |
| 8 | 730994620000260 | 2325810733931801 | 3056805353932061 | 3.594214 | Norman Luhn | 18 Jan 2023 |
| 9 | 1178234306003644 | 6308411019731047 | 7486645325734691 | 4.229453 | Norman Luhn | 18 Jan 2023 |
| 10 | 1308138316048410 | 11140102475962687 | 12448240792011097 | 3.939749 | Norman Luhn | 18 Jan 2023 |
| 11 | 1316489363200054 | 12448240792011097 | 13764730155211151 | 3.831580 | Norman Luhn | 18 Jan 2023 |
| 12 | 2165010689410800 | 14727257011031407 | 16892267700442207 | 5.932279 | Norman Luhn | 18 Jan 2023 |
| 13 | 2685175550882936 | 106920298210935941 | 109605473761818877 | 4.022344 | Norman Luhn | 18 Jan 2023 |
| 14 | 3393857853620850 | 124568430037136201 | 127962287890757051 | 4.850681 | Norman Luhn | 18 Jan 2023 |
| 15 | 3442769694870660 | 142977538681261357 | 146420308376132017 | 4.720759 | Norman Luhn | 18 Jan 2023 |
| 16 | 4539207862808850 | 216812607870223207 | 221351815733032057 | 5.491109 | Norman Luhn | 18 Jan 2023 |
| 17 | 6489192166738050 | 485616539165071387 | 492105731331809437 | 6.182247 | Norman Luhn | 18 Jan 2023 |
| 18 | 7310737867282080 | 842617217622945607 | 849927955490227687 | 5.931581 | Norman Luhn | 18 Jan 2023 |
| 19 | 11529242833092600 | 1035624071743706561 | 1047153314576799161 | 8.808118 | Norman Luhn | 18 Jan 2023 |
| 20 | 13627266591097886 | 2844738245030787221 | 2858365511621885107 | 7.806670 | Norman Luhn | 18 Jan 2023 |
| 21 | 14140332007226314 | 4081819125074525677 | 4095959457081751991 | 7.319850 | Norman Luhn | 18 Jan 2023 |
| 22 | 14281634215463726 | 4614246116693368271 | 4628527750908831997 | 7.144208 | Norman Luhn | 18 Jan 2023 |
| 23 | 15801916932897480 | 4837830340027454501 | 4853632256960351981 | 7.800831 | Norman Luhn | 18 Jan 2023 |
| 24 | 16391422592873516 | 6900205088923091831 | 6916596511515965347 | 7.332745 | Norman Luhn | 18 Jan 2023 |
| 25 | 17372520188668260 | 11473517342470328261 | 11490889862658996521 | 6.758179 | Norman Luhn | 18 Jan 2023 |
| 26 | 20577802367145870 | 12908144983107039551 | 12928722785474185421 | 7.751564 | Norman Luhn | 18 Jan 2023 |
| 27 | 21562758888249810 | 22539011692840407607 | 22560574451728657417 | 6.984493 | Norman Luhn | 18 Jan 2023 |
| 28 | 29440648392325170 | 22972168192963624477 | 23001608841355949647 | 9.487094 | Norman Luhn | 18 Jan 2023 |
| 29 | 34220713277621366 | 34557112838351783411 | 34591333551629404777 | 9.884976 | Norman Luhn | 18 Jan 2023 |
| 30 | 34429768587069240 | 63015703346062757021 | 63050133114649826261 | 8.482311 | Norman Luhn | 18 Jan 2023 |
| 31 | 43643596540302716 | 80685261082594283231 | 80728904679134585947 | 10.07679 | Norman Luhn | 18 Jan 2023 |
| 32 | 49064452667579854 | 104907885468383778007 | 104956949921051357861 | 10.57815 | Norman Luhn | 18 Jan 2023 |
| 33 | 54642888354104820 | 118170152255853853271 | 118224795144207958091 | Norman Luhn | 18 Jan 2023 | |
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