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 2.383392Norman Luhn08 Nov 2022
2 12542467454838090 7933248530182091 20475715985020181 1.263484Norman Luhn08 Nov 2022
3 25492684566238890 49600456951571411 75093141517810301 1.525789Norman Luhn08 Nov 2022
4 34655213713571220 84653373093824651 119308586807395871 1.757946Norman Luhn08 Nov 2022
5 104801597855003280 197053322268438521 301854920123441801 3.968038Norman Luhn08 Nov 2022
6 108886783714608900 301854920123441801 410741703838050701 3.668406Norman Luhn08 Nov 2022
7 135484401790537800 1011183292256483231 1146667694047021031 3.206844Norman Luhn08 Nov 2022
8 168057963095763510 1261124760662461811 1429182723758225321 3.713110Norman Luhn08 Nov 2022
9 274008349772096940 2714563183649972771 2988571533422069711 4.800358Norman Luhn08 Nov 2022
10 394247637250686450 6732104937121609931 7126352574372296381 5.278195Norman Luhn08 Nov 2022
11 502310960604543090 16503428853844408361 17005739814448951451 5.175126Norman Luhn08 Nov 2022
12 728897282435472150 27840909337169924111 28569806619605396261 6.450151Norman Luhn08 Nov 2022
13 963614853392341920 31658235700764968411 32621850554157310331
8.210507
Norman Luhn08 Nov 2022
14 1070595888894001470 88285754933431810871 89356350822325812341 6.819286Norman Luhn08 Nov 2022
15 1136132171174671440 241328992559587807991 242465124730762479431 5.466622Norman Luhn08 Nov 2022
16 1449928468427619180 262984116873383190401 264434045341810809581 6.811788Norman Luhn08 Nov 2022
17 1636484465063688240 550352963634281703011 551989448099345391251 6.280555Norman Luhn08 Nov 2022
18 1643953714565172780 559839038491504206551 561482992206069379331 6.279976Norman Luhn08 Nov 2022
19 1694570855080834500 659480213123471164541 661174783978551999041 6.191924Norman Luhn08 Nov 2022
20 2178528276131767560 967502843004917073971 969681371281048841531 7.177772Norman Luhn08 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 1.336045Norman Luhn08 Nov 2022
2 24396931904995650 7582919852522851 31979851757518501 2.231231Norman Luhn08 Nov 2022
3 29929899218379930 49357906247864281 79287805466244211 1.774402Norman Luhn08 Nov 2022
4 38519643930137370 98147762882334001 136667406812471371 1.864572Norman Luhn08 Nov 2022
5 90546254839420380 210509800417460611 301056055256880991 3.397273Norman Luhn08 Nov 2022
6 169308379726685430 389259253111633741 558567632838319171 5.208776Norman Luhn08 Nov 2022
7 236618900917709310 1347418405454024971 1584037306371734281 5.091057Norman Luhn08 Nov 2022
8 323621085272936220 2111163574238602951 2434784659511539171 6.079107Norman Luhn08 Nov 2022
9 359560663683310320 11319107721272355841 11678668384955666161 4.139398Norman Luhn08 Nov 2022
10 477467457464506740 15649679824334150431 16127147281798657171 4.996506Norman Luhn08 Nov 2022
11 481868020130768040 17999933772365008531 18481801792495776571 4.842224Norman Luhn08 Nov 2022
12 506760588544270830 43410634002853781731 43917394591398052561 3.952564Norman Luhn08 Nov 2022
13 1002464823181411590 46053229940785921921 47055694763967333511 7.676281Norman Luhn08 Nov 2022
14 1020910889829911850 56819191579692796321 57840102469522708171 7.365002Norman Luhn08 Nov 2022
15 1026210659866512120 86922973561200641701 87949184221067153821 6.565711Norman Luhn08 Nov 2022
16 1094297271205087950 171453018236360595571 172547315507565683521 5.788904Norman Luhn08 Nov 2022
17 1174519474242534420 262974065406340562341 264148584880583096761 5.518766Norman Luhn08 Nov 2022
18 1307454090687694950 265204116380452763581 266511570471140458531 6.128676Norman Luhn08 Nov 2022
19 1346394775340935320 443140595522725834801 444486990298066770121 5.481850Norman Luhn08 Nov 2022
20 1347363744375788370 459171260433506745961 460518624177882534331 5.432844Norman Luhn08 Nov 2022
21 1743357163215997560 470835952003395283141 472579309166611280701 6.980832Norman Luhn08 Nov 2022
22 2632797739002261600 486048603696796944871 488681401435799206471
10.44881
Norman Luhn08 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 1.754229Norman Luhn08 Nov 2022
2 16124281254081000 5693002600430263 21817283854511263 1.945372Norman Luhn08 Nov 2022
3 26473662499043760 21817283854511263 48290946353555023 2.265782Norman Luhn08 Nov 2022
4 28413480210146850 70219878257874463 98633358468021313 1.790580Norman Luhn08 Nov 2022
5 61969809049400070 104814760374339133 166784569423739203 3.341880Norman Luhn08 Nov 2022
6 78730177433737830 184601252515266523 263331429949004353 3.598148Norman Luhn08 Nov 2022
7 91132729335836370 691563581691049003 782696311026885373 2.836908Norman Luhn08 Nov 2022
8 103155993457446930 841262446570150723 944418440027597653 3.022817Norman Luhn08 Nov 2022
9 125344042389818070 1435418401751859643 1560762444141677713 3.124053Norman Luhn08 Nov 2022
10 127539477632857290 1560762444141677713 1688301921774535003 3.099791Norman Luhn08 Nov 2022
11 156563142189704250 1947972090069482413 2104535232259186663 3.553872Norman Luhn08 Nov 2022
12 240269556366599760 3113129526175724173 3353399082542323933 4.725656Norman Luhn08 Nov 2022
13 245630710294239270 6295720503796570783 6541351214090810053 3.925593Norman Luhn08 Nov 2022
14 371215799677454550 8606340809959757983 8977556609637212533 5.399813Norman Luhn08 Nov 2022
15 392491356277920900 11632476991152854773 12024968347430775673 5.227644Norman Luhn08 Nov 2022
16 438128540034903900 12117444113444616883 12555572653479520783 5.763384Norman Luhn08 Nov 2022
17 497774998147537110 19047831082581266083 19545606080728803193 5.740340Norman Luhn08 Nov 2022
18 553139526755926110 46967173288653414733 47520312815409340843 4.920723Norman Luhn08 Nov 2022
19 657669869041515330 56007759559403607073 56665429428445122403 5.562979Norman Luhn08 Nov 2022
20 705935707488511500 78226957215753783373 78932892923242294873 5.431288Norman Luhn08 Nov 2022
21 822091207610544690 144459980066229753043 145282071273840297733 5.323108Norman Luhn08 Nov 2022
22 953661106647030600 148530171084735294973 149483832191382325573 6.126564Norman Luhn08 Nov 2022
23 1010525037103622040 198650585455321576513 199661110492425198553 5.987148Norman Luhn08 Nov 2022
24 1120205770696901070 230570423348721342823 231690629119418243893 6.368163Norman Luhn08 Nov 2022
25 1150182918368986320 247622282200154937193 248772465118523923513 6.410794Norman Luhn08 Nov 2022
26 1469991613784694000 276509199658266520063 277979191272051214063 7.946386Norman Luhn08 Nov 2022
27 1740156371800596750 495437525245041193933 497177681616841790683
8.017329
Norman Luhn08 Nov 2022
28 1798327840699662090 1235380939578429649123 1237179267419129311213 6.474459Norman Luhn08 Nov 2022
29 1873162655755419210 1271562934974191036113 1273436097629946455323 6.691975Norman Luhn08 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 0.324054Norman Luhn08 Nov 2022
2 16574469604763070 11987120084474369 28561589689237439 1.716423Norman Luhn08 Nov 2022
3 33759731057120250 28561589689237439 62321320746357689 2.643959Norman Luhn08 Nov 2022
4 38168781590557800 98551408299919409 136720189890477209 2.154039Norman Luhn08 Nov 2022
5 89015666867118810 136720189890477209 225735856757596019 4.369062Norman Luhn08 Nov 2022
6 124548702384686580 750865965801985049 875414668186671629 3.759420Norman Luhn08 Nov 2022
7 175498545163583460 991430689120774919 1166929234284358379 4.846832Norman Luhn08 Nov 2022
8 271010198540941860 4469645436294291269 4740655634835233129 4.787126Norman Luhn08 Nov 2022
9 285342186046537620 7736710453100864069 8022052639147401689 4.288611Norman Luhn08 Nov 2022
10 331152983019350310 19747406226714769619 20078559209734119929 3.783860Norman Luhn08 Nov 2022
11 428837417342604270 26077931807056304009 26506769224398908279 4.518570Norman Luhn08 Nov 2022
12 440491943219876730 28380467873442589739 28820959816662466469 4.529297Norman Luhn08 Nov 2022
13 481337448657934050 30617981105711113949 31099318554369047999 4.841442Norman Luhn08 Nov 2022
14 568130757540604440 50237733508947889739 50805864266488494179 4.957790Norman Luhn08 Nov 2022
15 674162174192699010 55385600939412797069 56059763113605496079 5.720372Norman Luhn08 Nov 2022
16 997544746996687890 65094957110159161019 66092501857155848909 8.079364Norman Luhn08 Nov 2022
17 1041590211260008410 140331003847396286759 141372594058656295169 6.797750Norman Luhn08 Nov 2022
18 1278829158713586480 258669503755494985169 259948332914208571649 7.041976Norman Luhn08 Nov 2022
19 2141150123367765510 281791897446595228709 283933047569962994219
11.51055
Norman Luhn08 Nov 2022
20 2622130286984216190 628433489614526260499 631055619901510476689 11.32282Norman Luhn08 Nov 2022
21 2761891049962734690 1227483988372594877759 1230245879422557612449 9.959570Norman Luhn08 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 0.282520Norman Luhn08 Nov 2022
2 6484438776441780 4422879865247923 10907318641689703 0.788408Norman Luhn08 Nov 2022
3 21564983487367320 10907318641689703 32472302129057023 1.831671Norman Luhn08 Nov 2022
4 25286250608198580 67893346321234513 93179596929433093 1.348616Norman Luhn08 Nov 2022
5 66079878230746380 166362638531783773 232442516762530153 2.613115Norman Luhn08 Nov 2022
6 104386569904977360 571154954398178383 675541524303155743 2.856198Norman Luhn08 Nov 2022
7 136769138225633760 976957165062198553 1113726303287832313 3.178731Norman Luhn08 Nov 2022
8 333007764767307630 1432795262772323683 1765803027539631313 6.781860Norman Luhn08 Nov 2022
9 502739544062685930 8350561098813457603 8853300642876143533 6.134151Norman Luhn08 Nov 2022
10 561389904918946950 20112541874070035623 20673931778988982573 5.308430Norman Luhn08 Nov 2022
11 833568056800058580 25262425614686550523 26095993671486609103 7.369765Norman Luhn08 Nov 2022
12 865552701207047700 33279559021674315583 34145111722881363283 7.071698Norman Luhn08 Nov 2022
13 1302380821150909500 99263437927730670673 100565818748881580173 7.801345Norman Luhn08 Nov 2022
14 1304183386407471570 127867735193930732233 129171918580338203803 7.277583Norman Luhn08 Nov 2022
15 1309956937061362590 264531703877024964613 265841660814086327203 5.974014Norman Luhn08 Nov 2022
16 1518496317863064540 465337196844093354013 466855693161956418553 5.930885Norman Luhn08 Nov 2022
17 2538914834567671560 503755588248729670933 506294503083297342493 9.701656Norman Luhn08 Nov 2022
18 2723712973866284400 628289852614405051303 631013565588271335703
9.801620
Norman Luhn08 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 2.296519Norman Luhn08 Nov 2022
2 47315337066237240 22443709342850669 69759046409087909 3.108015Norman Luhn08 Nov 2022
3 70457661412794810 94415460183744419 164873121596539229 3.220633Norman Luhn08 Nov 2022
4 79686427365488790 608687580745239869 688374008110728659 2.152649Norman Luhn08 Nov 2022
5 92051064365119860 802397917781329589 894448982146449449 2.284164Norman Luhn08 Nov 2022
6 95754032642268000 999318084430035089 1095072117072303089 2.223899Norman Luhn08 Nov 2022
7 132593402211600330 1095072117072303089 1227665519283903419 2.981617Norman Luhn08 Nov 2022
8 256103879539844490 1617474865049032709 1873578744588877199 5.074271Norman Luhn08 Nov 2022
9 404430744117243690 3670004307958364249 4074435052075607939 6.275190Norman Luhn08 Nov 2022
10 493429637036129640 25597045215152406869 26090474852188536509 4.354379Norman Luhn08 Nov 2022
11 521795047286937270 27956220724939763129 28478015772226700399 4.488634Norman Luhn08 Nov 2022
12 530109013916235600 38775226124695075889 39305335138611311489 4.151436Norman Luhn08 Nov 2022
13 1092152270917103550 42241516093604867759 43333668364521971309
8.330293
Norman Luhn08 Nov 2022
14 1439121860781188430 218673443269428603329 220112565130209791759 6.916903Norman Luhn08 Nov 2022
15 1560714825194454930 301643778747539884529 303204493572734339459 6.864043Norman Luhn08 Nov 2022
16 1634335015941157530 410649344369935630679 412283679385876788209 6.604738Norman Luhn08 Nov 2022
17 2048887619218366080 600918486667094505629 602967374286312871709 7.463844Norman Luhn08 Nov 2022
18 2233638226940140020 744481922826413431379 746715561053353571399 7.678192Norman Luhn08 Nov 2022
19 2449084290683364180 1279096982834661496379 1281546067125344860559 7.279296Norman Luhn08 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