← Record Gaps Between Prime 12-tuplets

Pattern d: d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42
_{Gap end} 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	10.58145	Norman Luhn	08 Nov 2022
Maximal gaps below 1.499 · 10²⁰

Pattern d: d = 0, 6, 10, 12, 16, 22, 24, 30, 34, 36, 40, 42
_{Gap end} 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	11.44633	Norman Luhn	08 Nov 2022
Maximal gaps below 1.478 · 10²⁰

Record Gaps Between Prime 12-tuplets Over All Patterns

_{Gap end} 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	11.42185	Norman Luhn	18 Jan 2023
Maximal gaps below 1.478 · 10²⁰