←
Record Gaps Between Prime 10-tuplets

References: OEIS A202281 & OEIS A202361

Pattern d: d = 0, 2, 6, 8, 12, 18, 20, 26, 30, 32
Gap end
merit = 1704.74094019 ·∫dt / log10 t
Gap start
Rank
Gap Size
Gap start
Next Prime 10-tuplet
Merit
Who
When
1
33081664140
 11 33081664151
2.667166
Alexei Kourbatov
2011
2
50040961320
 33081664151 83122625471
0.994128
Alexei Kourbatov
2011
3
211797665730
 83122625471 294920291201
2.678628
Alexei Kourbatov
2011
4
278538937950
 294920291201 573459229151
2.510742
Alexei Kourbatov
2011
5
314694286830
 730121110331 1044815397161
2.165479
Alexei Kourbatov
2011
6
446820068310
 1291458592421 1738278660731
2.534051
Alexei Kourbatov
2011
7
589320949140
 4700094892301 5289415841441
2.200102
Alexei Kourbatov
2011
8
1135263664920
 6218504101541 7353767766461
3.819603
Alexei Kourbatov
2011
9
1154348695500
 7908189600581 9062538296081
3.601257
Alexei Kourbatov
2011
10
1280949740070
 10527733922591 11808683662661
3.645087
Alexei Kourbatov
2011
11
1340804150070
 21939572224301 23280376374371
3.024709
Alexei Kourbatov
2011
12
1458168320490
 23960929422161 25419097742651
3.196785
Alexei Kourbatov
2011
13
1539906870810
 30491978649941 32031885520751
3.128103
Alexei Kourbatov
2011
14
1858581264540
 46950720918371 48809302182911
3.294464
Alexei Kourbatov
2011
15
2590180927950
 84254447788781 86844628716731
3.825040
Alexei Kourbatov
2011
16
3182865274050
 118565337622001 121748202896051
4.230348
Alexei Kourbatov
2011
17
4949076176310
 124788318636251 129737394812561
6.462460
Alexei Kourbatov
2011
18
5719502339670
 235474768767851 241194271107521
6.167721
Alexei Kourbatov
2011
19
6474403830510
 513639397576421 520113801406931
5.540843
Alexei Kourbatov
2011
20
10176655910190
 826551814786541 836728470696731
7.575968
Alexei Kourbatov
2011
21
10696394997750
 1811660166341561 1822356561339311
6.358824
Alexei Kourbatov
2011
22
14795015572260
 3336445098184811 3351240113757071
7.404776
Alexei Kourbatov
2011
23
22064686726740
 4860936813525251 4883001500251991
9.945013
Alexei Kourbatov
2011
24
24115450098390
 15162739669803611 15186855119902001
7.974625
Dana Jacobsen
08 Oct 2015
25
24192886714920
 23067980938007891 23092173824722811
7.153143
Dana Jacobsen
08 Oct 2015
26
24591587339550
 24106673293158341 24131264880497891
7.186604
Dana Jacobsen
08 Oct 2015
27
25414002284790
 27954449769700451 27979863771985241
7.141681
Dana Jacobsen
08 Oct 2015
28
27094875302460
 38288339680738991 38315434556041451
7.009708
Dana Jacobsen
08 Oct 2015
29
28233128613690
 40130110778032391 40158343906646081
7.214925
Dana Jacobsen
08 Oct 2015
30
31265097203340
 52378829022364961 52410094119568301
7.453910
Dana Jacobsen
08 Oct 2015
31
32621645366310
 63951926022250151 63984547667616461
7.385382
Dana Jacobsen
08 Oct 2015
32
34366816437030
 76090775717546321 76125142533983351
7.439580
Dana Jacobsen
08 Oct 2015
33
53806886003640
 84230691483025931 84284498369029571
11.34739
Norman Luhn
2022
34
54756148657980
 206574042251081621 206628798399739601
9.197631
Norman Luhn
2022
35
57023329492710
 232683119626392971 232740142955885681
9.297185
Norman Luhn
2022
36
58293842234670
 272049159284490431 272107453126725101
9.140730
Norman Luhn
2022
37
67701164879040
 383594149345575011 383661850510454051
9.748617
Norman Luhn
2022
38
85058270058300
 472204560412317191 472289618682375491
11.63664
Norman Luhn
2022
39
86902828229490
 772731971300912081 772818874129141571
10.54155
Norman Luhn
2022
40
87203305981680
 813760732255935461 813847935561917141
10.44605
Norman Luhn
2022
41
111075798025500
 1312634110147655831 1312745185945681331
11.85712
Norman Luhn
2022
42
115583745947670
 2165124028389169691 2165239612135117361
10.95145
Norman Luhn
2022
43
126364209327930
 2194796268951211811 2194922633160539741
11.93436
Norman Luhn
2022
44
129378911789400
 3203465390775948911 3203594769687738311
11.17703
Norman Luhn
2022
45
131909992788000
 3518199226611987761 3518331136604775761
11.14807
Norman Luhn
2022
46
140852998350330
 4576306164780990371 4576447017779340701
11.19514
Norman Luhn
2022
47
172086775032480
 5046800897460287501 5046972984235319981
13.36998
Norman Luhn
2022
48
187976478509820
 8041249390631324711 8041437367109834531
13.11483
Norman Luhn
2022
49
192724233768990
 8136072077001093761 8136264801234862751
13.40992
Norman Luhn
2022
50
219864719393970
 10802377945240927931 10802597809960321901
14.33722
Norman Luhn
2022
51
222236783161470
 18762686717230305581 18762908954013467051
12.78666
Norman Luhn
2022
52
249391227445710
 27005520095579280791 27005769486806726501
13.22298
Norman Luhn
2022
53
283327601834550
 28024070637973418621 28024353965575253171
14.89858
Norman Luhn
2022
54
348608199064860
 48096357820756711001 48096706428955775861
16.26004
Norman Luhn
2022
Maximal gaps below 1.00 · 1020

Pattern d: d = 0, 2, 6, 12, 14, 20, 24, 26, 30, 32
Gap end
merit = 1704.74094019 ·∫dt / log10 t
Gap start
Rank
Gap Size
Gap start
Next Prime 10-tuplet
Merit
Who
When
1
12102794130
 9853497737 21956291867
0.409899
Alexei Kourbatov
2011
2
141702673770
 22741837817 164444511587
2.452639
Alexei Kourbatov
2011
3
424052301750
 242360943257 666413245007
3.801317
Alexei Kourbatov
2011
4
699699330330
 1418575498577 2118274828907
3.761184
Alexei Kourbatov
2011
5
714303547230
 4396774576277 5111078123507
2.712654
Alexei Kourbatov
2011
6
739544215410
 8639103445097 9378647660507
2.260777
Alexei Kourbatov
2011
7
1623198312120
 11105292314087 12728490626207
4.520873
Alexei Kourbatov
2011
8
2691533434590
 12728490626207 15420024060797
7.096803
Alexei Kourbatov
2011
9
4207848555330
 119057768524127 123265617079457
5.608461
Alexei Kourbatov
2011
10
4936074819480
 226608256438997 231544331258477
5.387015
Alexei Kourbatov
2011
11
5887574660310
 581653272077387 587540846737697
4.859124
Alexei Kourbatov
2011
12
6562654104930
 896217252921227 902779907026157
4.775374
Alexei Kourbatov
2011
13
7205070907650
 987041423819807 994246494727457
5.098115
Alexei Kourbatov
2011
14
8129061524010
 1408999953009347 1417129014533357
5.192414
Alexei Kourbatov
2011
15
8362548652500
 1419018243046487 1427380791698987
5.330623
Alexei Kourbatov
2011
16
9741706748970
 2189095026865907 2198836733614877
5.489526
Alexei Kourbatov
2011
17
9967327212570
 2274112300607657 2284079627820227
5.556493
Alexei Kourbatov
2011
18
11684428585830
 2369286971460107 2380971400045937
6.438189
Alexei Kourbatov
2011
19
15038225224680
 4498231210741967 4513269435966647
6.926430
Alexei Kourbatov
2011
20
16217864803140
 5320814086365287 5337031951168427
7.130761
Alexei Kourbatov
2011
21
18575781834960
 5406353435580257 5424929217415217
8.131185
Alexei Kourbatov
2011
22
19306163758770
 16042498396488647 16061804560247417
6.288748
Dana Jacobsen
09 Oct 2015
23
25095634366530
 16413611778830237 16438707413196767
8.124311
Dana Jacobsen
09 Oct 2015
24
39545602368930
 24115852659843797 24155398262212727
11.55462
Dana Jacobsen
09 Oct 2015
25
48720281559600
 89513460847628327 89562181129187927
10.11579
Dana Jacobsen
09 Oct 2015
26
49088149953570
 249706626550645697 249755714700599267
7.863511
Dana Jacobsen
09 Oct 2015
27
73039126470660
 252334218242220197 252407257368690857
11.66959
Dana Jacobsen
09 Oct 2015
28
84862268470980
 409980597881494877 410065460149965857
12.02070
Norman Luhn
2022
29
88674896279970
 459549985389505247 459638660285785217
12.21268
Norman Luhn
2022
30
98828283164730
 850162482392237867 850261310675402597
11.71370
Norman Luhn
2022
31
99379120794030
 867743248658993867 867842627779787897
11.72075
Norman Luhn
2022
32
104981228872170
 1742439788052087557 1742544769280959727
10.47336
Norman Luhn
2022
33
105381420647160
 1967887916683027037 1967993298103674197
10.21353
Norman Luhn
2022
34
118062260244390
 1991449734387443567 1991567796647687957
11.41026
Norman Luhn
2022
35
119651645205750
 2651786817266912177 2651906468912117927
10.80655
Norman Luhn
2022
36
124205963696010
 3333008320509918287 3333132526473614297
10.63082
Norman Luhn
2022
37
132065766534240
 3372261596377399697 3372393662143933937
11.27256
Norman Luhn
2022
38
144742887894990
 4456103544004414427 4456248286892309417
11.57582
Norman Luhn
2022
39
148258967439240
 5961697284185251307 5961845543152690547
11.08246
Norman Luhn
2022
40
159767457698310
 6212296237253972837 6212456004711671147
11.82957
Norman Luhn
2022
41
203116053488040
 7674412248597541607 7674615364651029647
14.32399
Norman Luhn
2022
42
213134282372130
 11159429144746883237 11159642279029255367
13.79563
Norman Luhn
2022
43
238811218681770
 17361488884282641797 17361727695501323567
13.98292
Norman Luhn
2022
44
242555605272330
 34156229483639927747 34156472039245200077
12.20445
Norman Luhn
2022
45
246390567159240
 42790693626498822857 42790940017065982097
11.79298
Norman Luhn
2022
46
273205564407930
 46202857341928072757 46203130547492480687
12.85654
Norman Luhn
2022
47
311901158216340
 51127920150885492347 51128232052043708687
14.35316
Norman Luhn
2022
48
313237605327570
 67889403750965583947 67889716988570911517
13.54420
Norman Luhn
2022
49
318544756263930
 72428660098860185357 72428978643616449287
13.57997
Norman Luhn
2022
Maximal gaps below 1.00 · 1020


Record Gaps Between Prime 10-tuplets Over All Patterns


Gap end
merit = 3409.48188039 ·∫dt / log10 t
Gap start
Rank
Gap Size
Gap start
Next Prime 10-tuplet
Merit
Who
When
1
9853497726
 11 9853497737
3.923225
Norman Luhn
18 Jan 2023
2
12102794130
 9853497737 21956291867
0.819798
Norman Luhn
18 Jan 2023
3
50040961320
 33081664151 83122625471
1.988256
Norman Luhn
18 Jan 2023
4
81321886116
 83122625471 164444511587
2.371066
Norman Luhn
18 Jan 2023
5
278538937950
 294920291201 573459229151
5.021484
Norman Luhn
18 Jan 2023
6
319703162154
 1418575498577 1738278660731
3.570108
Norman Luhn
18 Jan 2023
7
374567507580
 3699811791647 4074379299227
3.047990
Norman Luhn
18 Jan 2023
8
410983231206
 4700094892301 5111078123507
3.087185
Norman Luhn
18 Jan 2023
9
563272830120
 6390526086797 6953798916917
3.810525
Norman Luhn
18 Jan 2023
10
703391348574
 11105292314087 11808683662661
3.968595
Norman Luhn
18 Jan 2023
11
728748575256
 20933920839101 21662669414357
3.352404
Norman Luhn
18 Jan 2023
12
1458168320490
 23960929422161 25419097742651
6.393570
Norman Luhn
18 Jan 2023
13
2690434371924
 119057768524127 121748202896051
7.147176
Norman Luhn
18 Jan 2023
14
3036596580204
 279787876907237 282824473487441
6.229994
Norman Luhn
18 Jan 2023
15
3141561078810
 285539202502637 288680763581447
6.405914
Norman Luhn
18 Jan 2023
16
3362913297504
 555343131317057 558706044614561
5.630437
Norman Luhn
18 Jan 2023
17
3407968063500
 829367805582287 832775773645787
5.075094
Norman Luhn
18 Jan 2023
18
4358939581920
 872322923004341 876681862586261
6.395796
Norman Luhn
18 Jan 2023
19
4660763832426
 898119143193731 902779907026157
6.780810
Norman Luhn
18 Jan 2023
20
5093857694046
 1558072653622601 1563166511316647
6.324964
Norman Luhn
18 Jan 2023
21
5282087928546
 1677786567870221 1683068655798767
6.421617
Norman Luhn
18 Jan 2023
22
6011287324614
 1888531104078317 1894542391402931
7.065955
Norman Luhn
18 Jan 2023
23
6734090115324
 3049075116536147 3055809206651471
6.915080
Norman Luhn
18 Jan 2023
24
13040253984450
 4499162039650121 4512202293634571
12.01242
Norman Luhn
18 Jan 2023
25
13279237325970
 15167297271417647 15180576508743617
8.782631
Norman Luhn
18 Jan 2023
26
13574096572626
 21367378474780181 21380952571352807
8.192379
Norman Luhn
18 Jan 2023
27
15412220654094
 24115852659843797 24131264880497891
9.007628
Norman Luhn
18 Jan 2023
28
16665755852130
 34469249821245971 34485915577098101
8.864378
Norman Luhn
18 Jan 2023
29
22726140274950
 37423405897013021 37446132037287971
11.82970
Norman Luhn
18 Jan 2023
30
23094517277106
 75468950570776571 75492045088053677
10.02012
Norman Luhn
18 Jan 2023
31
24796207364040
 84255638044289837 84280434251653877
10.45827
Norman Luhn
18 Jan 2023
32
30228433744740
 124641828165146417 124672056598891157
11.53650
Norman Luhn
18 Jan 2023
33
31470119943990
 241668103762660007 241699573882603997
10.16531
Norman Luhn
18 Jan 2023
34
34045404413370
 387343710445857701 387377755850271071
9.781306
Norman Luhn
18 Jan 2023
35
40689122583690
 410007925926634571 410048615049218261
11.52716
Norman Luhn
18 Jan 2023
36
41310834926130
 556788093874787891 556829404709714021
10.85581
Norman Luhn
18 Jan 2023
37
71685014583576
 704427611935812881 704499296950396457
17.78683
Norman Luhn
18 Jan 2023
38
86401604779140
 3406851435021026801 3406937836625805941
14.71452
Norman Luhn
18 Jan 2023
39
103494438996324
 4155648846458506907 4155752340897503231
16.82549
Norman Luhn
18 Jan 2023
40
134488362002610
 17149680820650628487 17149815309012631097
15.79289
Norman Luhn
18 Jan 2023
41
145829716755294
 33479418916191326777 33479564745908082071
14.74063
Norman Luhn
18 Jan 2023
42
149895894350004
 55269292747619935067 55269442643514285071
13.56135
Norman Luhn
18 Jan 2023
43
217384583979990
 70872880635147649757 70873098019731629747
18.62301
Norman Luhn
18 Jan 2023
Maximal gaps below 1.00 · 1020