← Record Gaps Between Prime 13-tuplets

Pattern d: d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48
_{Gap end} merit = 25807.9800998 ·_∫dt / log¹³ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 13-tuplet	Merit	Who	When
1	7933248530182080	11	7933248530182091	2.383392	Norman Luhn	08 Nov 2022
2	12542467454838090	7933248530182091	20475715985020181	1.263484	Norman Luhn	08 Nov 2022
3	25492684566238890	49600456951571411	75093141517810301	1.525789	Norman Luhn	08 Nov 2022
4	34655213713571220	84653373093824651	119308586807395871	1.757946	Norman Luhn	08 Nov 2022
5	104801597855003280	197053322268438521	301854920123441801	3.968038	Norman Luhn	08 Nov 2022
6	108886783714608900	301854920123441801	410741703838050701	3.668406	Norman Luhn	08 Nov 2022
7	135484401790537800	1011183292256483231	1146667694047021031	3.206844	Norman Luhn	08 Nov 2022
8	168057963095763510	1261124760662461811	1429182723758225321	3.713110	Norman Luhn	08 Nov 2022
9	274008349772096940	2714563183649972771	2988571533422069711	4.800358	Norman Luhn	08 Nov 2022
10	394247637250686450	6732104937121609931	7126352574372296381	5.278195	Norman Luhn	08 Nov 2022
11	502310960604543090	16503428853844408361	17005739814448951451	5.175126	Norman Luhn	08 Nov 2022
12	728897282435472150	27840909337169924111	28569806619605396261	6.450151	Norman Luhn	08 Nov 2022
13	963614853392341920	31658235700764968411	32621850554157310331	8.210507	Norman Luhn	08 Nov 2022
14	1070595888894001470	88285754933431810871	89356350822325812341	6.819286	Norman Luhn	08 Nov 2022
15	1136132171174671440	241328992559587807991	242465124730762479431	5.466622	Norman Luhn	08 Nov 2022
16	1449928468427619180	262984116873383190401	264434045341810809581	6.811788	Norman Luhn	08 Nov 2022
17	1636484465063688240	550352963634281703011	551989448099345391251	6.280555	Norman Luhn	08 Nov 2022
18	1643953714565172780	559839038491504206551	561482992206069379331	6.279976	Norman Luhn	08 Nov 2022
19	1694570855080834500	659480213123471164541	661174783978551999041	6.191924	Norman Luhn	08 Nov 2022
20	2178528276131767560	967502843004917073971	969681371281048841531	7.177772	Norman Luhn	08 Nov 2022
Maximal gaps below 1.16 · 10²¹

Pattern d: d = 0, 6, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 48
_{Gap end} merit = 25807.9800998 ·_∫dt / log¹³ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 13-tuplet	Merit	Who	When
1	7396459235926530	186460616596321	7582919852522851	1.336045	Norman Luhn	08 Nov 2022
2	24396931904995650	7582919852522851	31979851757518501	2.231231	Norman Luhn	08 Nov 2022
3	29929899218379930	49357906247864281	79287805466244211	1.774402	Norman Luhn	08 Nov 2022
4	38519643930137370	98147762882334001	136667406812471371	1.864572	Norman Luhn	08 Nov 2022
5	90546254839420380	210509800417460611	301056055256880991	3.397273	Norman Luhn	08 Nov 2022
6	169308379726685430	389259253111633741	558567632838319171	5.208776	Norman Luhn	08 Nov 2022
7	236618900917709310	1347418405454024971	1584037306371734281	5.091057	Norman Luhn	08 Nov 2022
8	323621085272936220	2111163574238602951	2434784659511539171	6.079107	Norman Luhn	08 Nov 2022
9	359560663683310320	11319107721272355841	11678668384955666161	4.139398	Norman Luhn	08 Nov 2022
10	477467457464506740	15649679824334150431	16127147281798657171	4.996506	Norman Luhn	08 Nov 2022
11	481868020130768040	17999933772365008531	18481801792495776571	4.842224	Norman Luhn	08 Nov 2022
12	506760588544270830	43410634002853781731	43917394591398052561	3.952564	Norman Luhn	08 Nov 2022
13	1002464823181411590	46053229940785921921	47055694763967333511	7.676281	Norman Luhn	08 Nov 2022
14	1020910889829911850	56819191579692796321	57840102469522708171	7.365002	Norman Luhn	08 Nov 2022
15	1026210659866512120	86922973561200641701	87949184221067153821	6.565711	Norman Luhn	08 Nov 2022
16	1094297271205087950	171453018236360595571	172547315507565683521	5.788904	Norman Luhn	08 Nov 2022
17	1174519474242534420	262974065406340562341	264148584880583096761	5.518766	Norman Luhn	08 Nov 2022
18	1307454090687694950	265204116380452763581	266511570471140458531	6.128676	Norman Luhn	08 Nov 2022
19	1346394775340935320	443140595522725834801	444486990298066770121	5.481850	Norman Luhn	08 Nov 2022
20	1347363744375788370	459171260433506745961	460518624177882534331	5.432844	Norman Luhn	08 Nov 2022
21	1743357163215997560	470835952003395283141	472579309166611280701	6.980832	Norman Luhn	08 Nov 2022
22	2632797739002261600	486048603696796944871	488681401435799206471	10.44881	Norman Luhn	08 Nov 2022
Maximal gaps below 1.32 · 10²¹

Pattern d: d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48
_{Gap end} merit = 30109.31011644 ·_∫dt / log¹³ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 13-tuplet	Merit	Who	When
1	4289907938811600	13	4289907938811613	1.754229	Norman Luhn	08 Nov 2022
2	16124281254081000	5693002600430263	21817283854511263	1.945372	Norman Luhn	08 Nov 2022
3	26473662499043760	21817283854511263	48290946353555023	2.265782	Norman Luhn	08 Nov 2022
4	28413480210146850	70219878257874463	98633358468021313	1.790580	Norman Luhn	08 Nov 2022
5	61969809049400070	104814760374339133	166784569423739203	3.341880	Norman Luhn	08 Nov 2022
6	78730177433737830	184601252515266523	263331429949004353	3.598148	Norman Luhn	08 Nov 2022
7	91132729335836370	691563581691049003	782696311026885373	2.836908	Norman Luhn	08 Nov 2022
8	103155993457446930	841262446570150723	944418440027597653	3.022817	Norman Luhn	08 Nov 2022
9	125344042389818070	1435418401751859643	1560762444141677713	3.124053	Norman Luhn	08 Nov 2022
10	127539477632857290	1560762444141677713	1688301921774535003	3.099791	Norman Luhn	08 Nov 2022
11	156563142189704250	1947972090069482413	2104535232259186663	3.553872	Norman Luhn	08 Nov 2022
12	240269556366599760	3113129526175724173	3353399082542323933	4.725656	Norman Luhn	08 Nov 2022
13	245630710294239270	6295720503796570783	6541351214090810053	3.925593	Norman Luhn	08 Nov 2022
14	371215799677454550	8606340809959757983	8977556609637212533	5.399813	Norman Luhn	08 Nov 2022
15	392491356277920900	11632476991152854773	12024968347430775673	5.227644	Norman Luhn	08 Nov 2022
16	438128540034903900	12117444113444616883	12555572653479520783	5.763384	Norman Luhn	08 Nov 2022
17	497774998147537110	19047831082581266083	19545606080728803193	5.740340	Norman Luhn	08 Nov 2022
18	553139526755926110	46967173288653414733	47520312815409340843	4.920723	Norman Luhn	08 Nov 2022
19	657669869041515330	56007759559403607073	56665429428445122403	5.562979	Norman Luhn	08 Nov 2022
20	705935707488511500	78226957215753783373	78932892923242294873	5.431288	Norman Luhn	08 Nov 2022
21	822091207610544690	144459980066229753043	145282071273840297733	5.323108	Norman Luhn	08 Nov 2022
22	953661106647030600	148530171084735294973	149483832191382325573	6.126464	Norman Luhn	08 Nov 2022
23	1010525037103622040	198650585455321576513	199661110492425198553	5.987148	Norman Luhn	08 Nov 2022
24	1120205770696901070	230570423348721342823	231690629119418243893	6.368163	Norman Luhn	08 Nov 2022
25	1150182918368986320	247622282200154937193	248772465118523923513	6.410794	Norman Luhn	08 Nov 2022
26	1469991613784694000	276509199658266520063	277979191272051214063	7.946386	Norman Luhn	08 Nov 2022
27	1740156371800596750	495437525245041193933	497177681616841790683	8.017329	Norman Luhn	08 Nov 2022
28	1798327840699662090	1235380939578429649123	1237179267419129311213	6.474459	Norman Luhn	08 Nov 2022
29	1873162655755419210	1271562934974191036113	1273436097629946455323	6.691975	Norman Luhn	08 Nov 2022
Maximal gaps below 1.29 · 10²¹

Pattern d: d = 0, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48
_{Gap end} merit = 30109.31011644 ·_∫dt / log¹³ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 13-tuplet	Merit	Who	When
1	2374023436926960	7697168877290909	10071192314217869	0.324054	Norman Luhn	08 Nov 2022
2	16574469604763070	11987120084474369	28561589689237439	1.716423	Norman Luhn	08 Nov 2022
3	33759731057120250	28561589689237439	62321320746357689	2.643959	Norman Luhn	08 Nov 2022
4	38168781590557800	98551408299919409	136720189890477209	2.154039	Norman Luhn	08 Nov 2022
5	89015666867118810	136720189890477209	225735856757596019	4.369062	Norman Luhn	08 Nov 2022
6	124548702384686580	750865965801985049	875414668186671629	3.759420	Norman Luhn	08 Nov 2022
7	175498545163583460	991430689120774919	1166929234284358379	4.846832	Norman Luhn	08 Nov 2022
8	271010198540941860	4469645436294291269	4740655634835233129	4.787126	Norman Luhn	08 Nov 2022
9	285342186046537620	7736710453100864069	8022052639147401689	4.288611	Norman Luhn	08 Nov 2022
10	331152983019350310	19747406226714769619	20078559209734119929	3.783860	Norman Luhn	08 Nov 2022
11	428837417342604270	26077931807056304009	26506769224398908279	4.518570	Norman Luhn	08 Nov 2022
12	440491943219876730	28380467873442589739	28820959816662466469	4.529297	Norman Luhn	08 Nov 2022
13	481337448657934050	30617981105711113949	31099318554369047999	4.841442	Norman Luhn	08 Nov 2022
14	568130757540604440	50237733508947889739	50805864266488494179	4.957790	Norman Luhn	08 Nov 2022
15	674162174192699010	55385600939412797069	56059763113605496079	5.720372	Norman Luhn	08 Nov 2022
16	997544746996687890	65094957110159161019	66092501857155848909	8.079364	Norman Luhn	08 Nov 2022
17	1041590211260008410	140331003847396286759	141372594058656295169	6.797750	Norman Luhn	08 Nov 2022
18	1278829158713586480	258669503755494985169	259948332914208571649	7.041976	Norman Luhn	08 Nov 2022
19	2141150123367765510	281791897446595228709	283933047569962994219	11.51055	Norman Luhn	08 Nov 2022
20	2622130286984216190	628433489614526260499	631055619901510476689	11.32282	Norman Luhn	08 Nov 2022
21	2761891049962734690	1227483988372594877759	1230245879422557612449	9.959570	Norman Luhn	08 Nov 2022
Maximal gaps below 1.29 · 10²¹

Pattern d: d = 0, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48
_{Gap end} merit = 25091.0917637013 ·_∫dt / log¹³ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 13-tuplet	Merit	Who	When
1	1558691309879550	1707898733581273	3266590043460823	0.282520	Norman Luhn	08 Nov 2022
2	6484438776441780	4422879865247923	10907318641689703	0.788408	Norman Luhn	08 Nov 2022
3	21564983487367320	10907318641689703	32472302129057023	1.831671	Norman Luhn	08 Nov 2022
4	25286250608198580	67893346321234513	93179596929433093	1.348616	Norman Luhn	08 Nov 2022
5	66079878230746380	166362638531783773	232442516762530153	2.613115	Norman Luhn	08 Nov 2022
6	104386569904977360	571154954398178383	675541524303155743	2.856198	Norman Luhn	08 Nov 2022
7	136769138225633760	976957165062198553	1113726303287832313	3.178731	Norman Luhn	08 Nov 2022
8	333007764767307630	1432795262772323683	1765803027539631313	6.781860	Norman Luhn	08 Nov 2022
9	502739544062685930	8350561098813457603	8853300642876143533	6.134151	Norman Luhn	08 Nov 2022
10	561389904918946950	20112541874070035623	20673931778988982573	5.308430	Norman Luhn	08 Nov 2022
11	833568056800058580	25262425614686550523	26095993671486609103	7.369765	Norman Luhn	08 Nov 2022
12	865552701207047700	33279559021674315583	34145111722881363283	7.071698	Norman Luhn	08 Nov 2022
13	1302380821150909500	99263437927730670673	100565818748881580173	7.801345	Norman Luhn	08 Nov 2022
14	1304183386407471570	127867735193930732233	129171918580338203803	7.277583	Norman Luhn	08 Nov 2022
15	1309956937061362590	264531703877024964613	265841660814086327203	5.974014	Norman Luhn	08 Nov 2022
16	1518496317863064540	465337196844093354013	466855693161956418553	5.930885	Norman Luhn	08 Nov 2022
17	2538914834567671560	503755588248729670933	506294503083297342493	9.701656	Norman Luhn	08 Nov 2022
18	2723712973866284400	628289852614405051303	631013565588271335703	9.801620	Norman Luhn	08 Nov 2022
Maximal gaps below 1.29 · 10²¹

Pattern d: d = 0, 2, 12, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48
_{Gap end} merit = 25091.0917637013 ·_∫dt / log¹³ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 13-tuplet	Merit	Who	When
1	15980558637817620	10527733922579	15991086371740199	2.296519	Norman Luhn	08 Nov 2022
2	47315337066237240	22443709342850669	69759046409087909	3.108015	Norman Luhn	08 Nov 2022
3	70457661412794810	94415460183744419	164873121596539229	3.220633	Norman Luhn	08 Nov 2022
4	79686427365488790	608687580745239869	688374008110728659	2.152649	Norman Luhn	08 Nov 2022
5	92051064365119860	802397917781329589	894448982146449449	2.284164	Norman Luhn	08 Nov 2022
6	95754032642268000	999318084430035089	1095072117072303089	2.223899	Norman Luhn	08 Nov 2022
7	132593402211600330	1095072117072303089	1227665519283903419	2.981617	Norman Luhn	08 Nov 2022
8	256103879539844490	1617474865049032709	1873578744588877199	5.074271	Norman Luhn	08 Nov 2022
9	404430744117243690	3670004307958364249	4074435052075607939	6.275190	Norman Luhn	08 Nov 2022
10	493429637036129640	25597045215152406869	26090474852188536509	4.354379	Norman Luhn	08 Nov 2022
11	521795047286937270	27956220724939763129	28478015772226700399	4.488634	Norman Luhn	08 Nov 2022
12	530109013916235600	38775226124695075889	39305335138611311489	4.151436	Norman Luhn	08 Nov 2022
13	1092152270917103550	42241516093604867759	43333668364521971309	8.330293	Norman Luhn	08 Nov 2022
14	1439121860781188430	218673443269428603329	220112565130209791759	6.916903	Norman Luhn	08 Nov 2022
15	1560714825194454930	301643778747539884529	303204493572734339459	6.864043	Norman Luhn	08 Nov 2022
16	1634335015941157530	410649344369935630679	412283679385876788209	6.604738	Norman Luhn	08 Nov 2022
17	2048887619218366080	600918486667094505629	602967374286312871709	7.463844	Norman Luhn	08 Nov 2022
18	2233638226940140020	744481922826413431379	746715561053353571399	7.678192	Norman Luhn	08 Nov 2022
19	2449084290683364180	1279096982834661496379	1281546067125344860559	7.279296	Norman Luhn	08 Nov 2022
Maximal gaps below 1.29 · 10²¹

Record Gaps Between Prime 13-tuplets Over All Patterns

_{Gap end} merit = 162016.7639599 ·_∫dt / log¹³ t ^{Gap start}
Rank	Gap Size	Gap start	Next Prime 13-tuplet	Merit	Who	When
1	2	11	13	2.449643	Norman Luhn	18 Jan 2023
2	10527733922566	13	10527733922579	3.058445	Norman Luhn	18 Jan 2023
3	175932882673742	10527733922579	186460616596321	0.799487	Norman Luhn	18 Jan 2023
4	1521438116984952	186460616596321	1707898733581273	2.735882	Norman Luhn	18 Jan 2023
5	1558691309879550	1707898733581273	3266590043460823	1.824274	Norman Luhn	18 Jan 2023
6	1889917252092588	5693002600430263	7582919852522851	1.539991	Norman Luhn	18 Jan 2023
7	2137943784035778	7933248530182091	10071192314217869	1.562519	Norman Luhn	18 Jan 2023
8	4003966287265830	11987120084474369	15991086371740199	2.507231	Norman Luhn	18 Jan 2023
9	4484629613279982	15991086371740199	20475715985020181	2.559407	Norman Luhn	18 Jan 2023
10	6117880346386770	22443709342850669	28561589689237439	3.108952	Norman Luhn	18 Jan 2023
11	6754736905115430	33502273017038711	40257009922154141	3.023781	Norman Luhn	18 Jan 2023
12	8033936431400882	40257009922154141	48290946353555023	3.379731	Norman Luhn	18 Jan 2023
13	10644108551235120	104814760374339133	115458868925574253	3.297588	Norman Luhn	18 Jan 2023
14	13456478149022090	197053322268438521	210509800417460611	3.405122	Norman Luhn	18 Jan 2023
15	29017043184746748	272039012072134243	301056055256880991	6.573877	Norman Luhn	18 Jan 2023
16	32832293265683730	1047475863642863773	1080308156908547503	4.898820	Norman Luhn	18 Jan 2023
17	44660207284402710	1443771785192736719	1488431992477139429	6.029227	Norman Luhn	18 Jan 2023
18	46306309576887080	1714532248479805871	1760838558056692951	5.930448	Norman Luhn	18 Jan 2023
19	49399108065501796	3270495071809685953	3319894179875187749	5.197445	Norman Luhn	18 Jan 2023
20	50091363404193150	4223113186660803269	4273204550064996419	4.878631	Norman Luhn	18 Jan 2023
21	61375960786358116	4345452296465505343	4406828257251863459	5.924182	Norman Luhn	18 Jan 2023
22	92239236683463870	4619280148472746693	4711519385156210563	8.732416	Norman Luhn	18 Jan 2023
23	93263356963666890	12304484935179522959	12397748292143189849	6.599116	Norman Luhn	18 Jan 2023
24	103444317228890536	13417585713157422733	13521030030386313269	7.134469	Norman Luhn	18 Jan 2023
25	116895417753906610	19142318145795018241	19259213563548924851	7.264248	Norman Luhn	18 Jan 2023
26	117532514082713730	47369052318358130593	47486584832440844323	5.619866	Norman Luhn	18 Jan 2023
27	130046758556844372	53916947360351371169	54046994118908215541	5.991837	Norman Luhn	18 Jan 2023
28	179230748794005090	55828528810609601983	56007759559403607073	8.175153	Norman Luhn	18 Jan 2023
29	205378412253903826	123821308453977238183	124026686866231142009	7.476269	Norman Luhn	18 Jan 2023
30	226082435436947806	124260428516214805933	124486510951651753739	8.221578	Norman Luhn	18 Jan 2023
31	229993366994554998	175809592423376487461	176039585790371042459	7.590128	Norman Luhn	18 Jan 2023
32	302624248968928590	241746935156728164179	242049559405697092769	9.141114	Norman Luhn	18 Jan 2023
33	346666274971826042	349121577868484646059	349468244143456472101	9.462034	Norman Luhn	18 Jan 2023
34	394146128902980300	739887265568046055693	740281411696949035993	8.766291	Norman Luhn	18 Jan 2023
35	505205471751015688	1018275345691180997653	1018780551162932013341	10.30932	Norman Luhn	18 Jan 2023
Maximal gaps below 1.164 · 10²¹