←
Record Gaps Between Prime Triplets

References: OEIS A201598 & OEIS A201596

Pattern d: d = 0, 2, 6
Gap end
merit = 2.85824859 ·∫dt / log3 t
Gap start
Rank
Gap Size
Gap start
Next Prime Triplet
Merit
Who
When
1
6
 5 11
2.133609
Alexei Kourbatov
2013
2
24
 17 41
1.911767
Alexei Kourbatov
2013
3
60
 41 101
2.315800
Alexei Kourbatov
2013
4
84
 107 191
1.944894
Alexei Kourbatov
2013
5
114
 347 461
1.511663
Alexei Kourbatov
2013
6
180
 461 641
2.053258
Alexei Kourbatov
2013
7
210
 881 1091
1.834584
Alexei Kourbatov
2013
8
264
 1607 1871
1.817856
Alexei Kourbatov
2013
9
390
 2267 2657
2.342545
Alexei Kourbatov
2013
10
564
 2687 3251
3.155969
Alexei Kourbatov
2013
11
630
 6197 6827
2.659703
Alexei Kourbatov
2013
12
1050
 6827 7877
4.255010
Alexei Kourbatov
2013
13
1200
 39227 40427
2.886135
Alexei Kourbatov
2013
14
1530
 46181 47711
3.513622
Alexei Kourbatov
2013
15
2016
 56891 58907
4.369179
Alexei Kourbatov
2013
16
2844
 83267 86111
5.564465
Alexei Kourbatov
2013
17
3426
 167621 171047
5.611133
Alexei Kourbatov
2013
18
3756
 375251 379007
5.071031
Alexei Kourbatov
2013
19
3864
 381527 385391
5.196608
Alexei Kourbatov
2013
20
3936
 549161 553097
4.869542
Alexei Kourbatov
2013
21
4074
 741677 745751
4.712461
Alexei Kourbatov
2013
22
4110
 805031 809141
4.668868
Alexei Kourbatov
2013
23
6090
 931571 937661
6.698988
Alexei Kourbatov
2013
24
8250
 2095361 2103611
7.643991
Alexei Kourbatov
2013
25
9240
 2428451 2437691
8.306285
Alexei Kourbatov
2013
26
9270
 4769111 4778381
7.284936
Alexei Kourbatov
2013
27
10344
 4938287 4948631
8.073806
Alexei Kourbatov
2013
28
10506
 12300641 12311147
6.901298
Alexei Kourbatov
2013
29
10734
 12652457 12663191
7.014660
Alexei Kourbatov
2013
30
10920
 13430171 13441091
7.058709
Alexei Kourbatov
2013
31
12930
 14094797 14107727
8.284542
Alexei Kourbatov
2013
32
15204
 18074027 18089231
9.313153
Alexei Kourbatov
2013
33
20190
 29480651 29500841
11.34180
Alexei Kourbatov
2013
34
20286
 107379731 107400017
9.169516
Alexei Kourbatov
2013
35
21216
 138778301 138799517
9.201664
Alexei Kourbatov
2013
36
25746
 156377861 156403607
10.95572
Alexei Kourbatov
2013
37
34920
 242419361 242454281
13.87012
Alexei Kourbatov
2013
38
38820
 913183487 913222307
12.63286
Alexei Kourbatov
2013
39
39390
 1139296721 1139336111
12.41472
Alexei Kourbatov
2013
40
41754
 2146630637 2146672391
12.02984
Alexei Kourbatov
2013
41
43020
 2188525331 2188568351
12.36120
Alexei Kourbatov
2013
42
44310
 3207540881 3207585191
12.07639
Alexei Kourbatov
2013
43
52500
 3577586921 3577639421
14.09652
Alexei Kourbatov
2013
44
71346
 7274246711 7274318057
17.41627
Alexei Kourbatov
2013
45
78114
 33115389407 33115467521
15.70835
Alexei Kourbatov
2013
46
80850
 97128744521 97128825371
14.27099
Alexei Kourbatov
2013
47
83040
 99216417017 99216500057
14.62065
Alexei Kourbatov
2013
48
83424
 103205810327 103205893751
14.61987
Alexei Kourbatov
2013
49
102330
 133645751381 133645853711
17.39578
Alexei Kourbatov
2013
50
109620
 373845384527 373845494147
16.55920
Alexei Kourbatov
2013
51
111450
 412647825677 412647937127
16.64985
Alexei Kourbatov
2013
52
131964
 413307596957 413307728921
19.71096
Alexei Kourbatov
2013
53
132756
 1368748574441 1368748707197
17.38783
Alexei Kourbatov
2013
54
137004
 1862944563707 1862944700711
17.36325
Alexei Kourbatov
2013
55
147186
 2368150202501 2368150349687
18.18636
Alexei Kourbatov
2013
56
148974
 2370801522107 2370801671081
18.40512
Alexei Kourbatov
2013
57
166050
 3710432509181 3710432675231
19.57697
Alexei Kourbatov
2013
58
174510
 5235737405807 5235737580317
19.85713
Alexei Kourbatov
2013
59
190920
 8615518909601 8615519100521
20.65269
Alexei Kourbatov
2013
60
194940
 10423696470287 10423696665227
20.68801
Alexei Kourbatov
2013
61
200574
 10660256412977 10660256613551
21.23819
Alexei Kourbatov
2013
62
207774
 11602981439237 11602981647011
21.81518
Alexei Kourbatov
2013
63
221526
 21824373608561 21824373830087
21.85312
Alexei Kourbatov
2013
64
241260
 36385356561077 36385356802337
22.65010
Alexei Kourbatov
2013
65
275280
 81232357111331 81232357386611
23.94812
Alexei Kourbatov
2013
66
276900
 186584419495421 186584419772321
22.30612
Alexei Kourbatov
2013
67
295470
 297164678680151 297164678975621
22.81869
Alexei Kourbatov
2013
68
298500
 428204300934581 428204301233081
22.31090
Alexei Kourbatov
2013
69
315006
 450907041535541 450907041850547
23.43664
Alexei Kourbatov
2013
70
334650
 464151342563471 464151342898121
24.83419
Alexei Kourbatov
2013
71
343266
 484860391301771 484860391645037
25.37506
Alexei Kourbatov
2013
72
352026
 666901733009921 666901733361947
25.30032
Alexei Kourbatov
2013
73
355650
 1039463608480391 1039463608836041
24.58911
Norman Luhn
19 Nov 2022
74
392370
 1440653814746297 1440653815138667
26.37393
Norman Luhn
20 Nov 2022
75
402456
 1516877715570671 1516877715973127
26.93236
Norman Luhn
20 Nov 2022
76
432600
 4492102614437111 4492102614869711
26.41147
Norman Luhn
12 Jan 2023
77
449520
 6410366769613991 6410366770063511
26.64792
Norman Luhn
20 Jan 2023
78
457380
 9984931182639311 9984931183096691
26.14710
Norman Luhn
24 Jan 2023
Maximal gaps below 1.00 · 1016


Pattern d: d = 0, 4, 6
Gap end
merit = 2.85824859 ·∫dt / log3 t
Gap start
Rank
Gap Size
Gap start
Next Prime Triplet
Merit
Who
When
1
6
 7 13
1.487867
Alexei Kourbatov
2013
2
24
 13 37
2.259527
Alexei Kourbatov
2013
3
30
 37 67
1.421217
Alexei Kourbatov
2013
4
90
 103 193
2.097659
Alexei Kourbatov
2013
5
150
 307 457
2.051352
Alexei Kourbatov
2013
6
156
 457 613
1.803388
Alexei Kourbatov
2013
7
210
 613 823
2.115861
Alexei Kourbatov
2013
8
240
 2137 2377
1.490314
Alexei Kourbatov
2013
9
306
 2377 2683
1.818426
Alexei Kourbatov
2013
10
366
 2797 3163
2.044171
Alexei Kourbatov
2013
11
384
 3463 3847
1.988321
Alexei Kourbatov
2013
12
444
 4783 5227
2.053592
Alexei Kourbatov
2013
13
810
 5737 6547
3.489471
Alexei Kourbatov
2013
14
834
 9433 10267
3.066475
Alexei Kourbatov
2013
15
1086
 14557 15643
3.484288
Alexei Kourbatov
2013
16
1200
 24103 25303
3.314686
Alexei Kourbatov
2013
17
1326
 45817 47143
3.053615
Alexei Kourbatov
2013
18
2316
 52177 54493
5.133861
Alexei Kourbatov
2013
19
3876
 126487 130363
6.806502
Alexei Kourbatov
2013
20
4230
 317587 321817
5.937212
Alexei Kourbatov
2013
21
4350
 580687 585037
5.313940
Alexei Kourbatov
2013
22
8244
 715873 724117
9.604895
Alexei Kourbatov
2013
23
8880
 2719663 2728543
7.801444
Alexei Kourbatov
2013
24
9450
 6227563 6237013
7.053163
Alexei Kourbatov
2013
25
10686
 8114857 8125543
7.584302
Alexei Kourbatov
2013
26
10950
 10085623 10096573
7.461739
Alexei Kourbatov
2013
27
11784
 10137493 10149277
8.022343
Alexei Kourbatov
2013
28
12816
 18773137 18785953
7.797258
Alexei Kourbatov
2013
29
13554
 21297553 21311107
8.062706
Alexei Kourbatov
2013
30
15504
 25291363 25306867
8.946535
Alexei Kourbatov
2013
31
15576
 43472497 43488073
8.183140
Alexei Kourbatov
2013
32
16254
 52645423 52661677
8.266475
Alexei Kourbatov
2013
33
16506
 69718147 69734653
8.009070
Alexei Kourbatov
2013
34
16596
 80002627 80019223
7.871469
Alexei Kourbatov
2013
35
19446
 89776327 89795773
9.050155
Alexei Kourbatov
2013
36
19944
 90338953 90358897
9.272428
Alexei Kourbatov
2013
37
21516
 109060027 109081543
9.701027
Alexei Kourbatov
2013
38
38340
 148770907 148809247
16.44479
Alexei Kourbatov
2013
39
39990
 1060162843 1060202833
12.73525
Alexei Kourbatov
2013
40
41556
 1327914037 1327955593
12.81292
Alexei Kourbatov
2013
41
45786
 2562574867 2562620653
12.87062
Alexei Kourbatov
2013
42
47190
 2985876133 2985923323
12.98837
Alexei Kourbatov
2013
43
48246
 4760009587 4760057833
12.46263
Alexei Kourbatov
2013
44
59856
 5557217797 5557277653
15.14376
Alexei Kourbatov
2013
45
62220
 10481744677 10481806897
14.47848
Alexei Kourbatov
2013
46
62286
 19587414277 19587476563
13.37663
Alexei Kourbatov
2013
47
65790
 25302582667 25302648457
13.68095
Alexei Kourbatov
2013
48
70980
 30944120407 30944191387
14.39430
Alexei Kourbatov
2013
49
72384
 37638900283 37638972667
14.32768
Alexei Kourbatov
2013
50
74664
 49356265723 49356340387
14.29630
Alexei Kourbatov
2013
51
81234
 49428907933 49428989167
15.55150
Alexei Kourbatov
2013
52
82566
 70192637737 70192720303
15.14992
Alexei Kourbatov
2013
53
90090
 74734558567 74734648657
16.40661
Alexei Kourbatov
2013
54
95466
 111228311647 111228407113
16.58292
Alexei Kourbatov
2013
55
100590
 134100150127 134100250717
17.09319
Alexei Kourbatov
2013
56
103224
 195126585733 195126688957
16.79249
Alexei Kourbatov
2013
57
106800
 239527477753 239527584553
16.96958
Alexei Kourbatov
2013
58
118440
 415890988417 415891106857
17.67858
Alexei Kourbatov
2013
59
127704
 688823669533 688823797237
18.02231
Alexei Kourbatov
2013
60
135390
 906056631937 906056767327
18.54197
Alexei Kourbatov
2013
61
138066
 926175746857 926175884923
18.86327
Alexei Kourbatov
2013
62
141846
 1157745737047 1157745878893
18.91637
Alexei Kourbatov
2013
63
146874
 1208782895053 1208783041927
19.49592
Alexei Kourbatov
2013
64
149334
 2124064384483 2124064533817
18.66473
Alexei Kourbatov
2013
65
153480
 2543551885573 2543552039053
18.82210
Alexei Kourbatov
2013
66
191070
 4321372168453 4321372359523
22.17459
Alexei Kourbatov
2013
67
199410
 6136808604343 6136808803753
22.32532
Alexei Kourbatov
2013
68
199860
 18292411110217 18292411310077
20.05973
Alexei Kourbatov
2013
69
220236
 19057076066317 19057076286553
22.01615
Alexei Kourbatov
2013
70
225324
 21794613251773 21794613477097
22.23075
Alexei Kourbatov
2013
71
238464
 35806145634613 35806145873077
22.42215
Alexei Kourbatov
2013
72
246174
 75359307977293 75359308223467
21.56728
Alexei Kourbatov
2013
73
251790
 89903831167897 89903831419687
21.69781
Alexei Kourbatov
2013
74
280740
 125428917151957 125428917432697
23.45567
Alexei Kourbatov
2013
75
287220
 194629563521143 194629563808363
23.04852
Alexei Kourbatov
2013
76
313350
 367947033766573 367947034079923
23.74001
Alexei Kourbatov
2013
77
333066
 376957618687747 376957619020813
25.17920
Alexei Kourbatov
2013
78
344634
 483633763994653 483633764339287
25.48191
Alexei Kourbatov
2013
79
386574
 539785800105313 539785800491887
28.30615
Alexei Kourbatov
2013
80
401286
 1413850739732107 1413850740133393
27.01683
Norman Luhn
22 Nov 2022
81
418644
 3540367390888183 3540367391306827
26.07272
Norman Luhn
15 Jan 2023
82
437184
 5106076704281803 5106076704718987
26.40871
Norman Luhn
16 Jan 2023
Maximal gaps below 1.00 · 1016


Record Gaps Between Prime Triplets Over All Patterns


Gap end
merit = 5.71649719 ·∫dt / log3 t
Gap start
Rank
Gap Size
Gap start
Next Prime Triplet
Merit
Who
When
1
2
 5 7
2.039345
Norman Luhn
16 Jan 2023
2
4
 7 11
2.227873
Norman Luhn
16 Jan 2023
3
20
 17 37
3.358156
Norman Luhn
16 Jan 2023
4
26
 41 67
2.377057
Norman Luhn
16 Jan 2023
5
30
 67 97
2.018857
Norman Luhn
16 Jan 2023
6
84
 107 191
3.889788
Norman Luhn
16 Jan 2023
7
110
 347 457
2.924012
Norman Luhn
16 Jan 2023
8
152
 461 613
3.507463
Norman Luhn
16 Jan 2023
9
180
 641 821
3.594853
Norman Luhn
16 Jan 2023
10
206
 881 1087
3.602303
Norman Luhn
16 Jan 2023
11
280
 2377 2657
3.334230
Norman Luhn
16 Jan 2023
12
366
 2797 3163
4.088342
Norman Luhn
16 Jan 2023
13
460
 5737 6197
4.002056
Norman Luhn
16 Jan 2023
14
546
 7207 7753
4.398218
Norman Luhn
16 Jan 2023
15
806
 9461 10267
5.924245
Norman Luhn
16 Jan 2023
16
1014
 14627 15641
6.501930
Norman Luhn
16 Jan 2023
17
1220
 60917 62137
5.201073
Norman Luhn
16 Jan 2023
18
1624
 77263 78887
6.493458
Norman Luhn
16 Jan 2023
19
1734
 95087 96821
6.566084
Norman Luhn
16 Jan 2023
20
1736
 291437 293173
4.978092
Norman Luhn
16 Jan 2023
21
1850
 406577 408427
4.906096
Norman Luhn
16 Jan 2023
22
2186
 408431 410617
5.790491
Norman Luhn
16 Jan 2023
23
2734
 444523 447257
7.100916
Norman Luhn
16 Jan 2023
24
3080
 1248347 1251427
6.363744
Norman Luhn
16 Jan 2023
25
3270
 1313953 1317223
6.682882
Norman Luhn
16 Jan 2023
26
3356
 1606541 1609897
6.573506
Norman Luhn
16 Jan 2023
27
3954
 2117233 2121187
7.313010
Norman Luhn
16 Jan 2023
28
4950
 2195861 2200811
9.086363
Norman Luhn
16 Jan 2023
29
5420
 2972897 2978317
9.355124
Norman Luhn
16 Jan 2023
30
5878
 4079683 4085561
9.526273
Norman Luhn
16 Jan 2023
31
5964
 5137787 5143751
9.239604
Norman Luhn
16 Jan 2023
32
5974
 7238377 7244351
8.665824
Norman Luhn
16 Jan 2023
33
7886
 9690347 9698233
10.82823
Norman Luhn
16 Jan 2023
34
8754
 18777047 18785801
10.65168
Norman Luhn
16 Jan 2023
35
8762
 29747561 29756323
9.829046
Norman Luhn
16 Jan 2023
36
10164
 41193793 41203957
10.77847
Norman Luhn
16 Jan 2023
37
11316
 47497991 47509307
11.71244
Norman Luhn
16 Jan 2023
38
11398
 57781693 57793091
11.41349
Norman Luhn
16 Jan 2023
39
15154
 116363077 116378231
13.52261
Norman Luhn
16 Jan 2023
40
15536
 214452521 214468057
12.57987
Norman Luhn
16 Jan 2023
41
15600
 327548717 327564317
11.83068
Norman Luhn
16 Jan 2023
42
17050
 369533497 369550547
12.69463
Norman Luhn
16 Jan 2023
43
19376
 437415521 437434897
14.06272
Norman Luhn
16 Jan 2023
44
20936
 1077020801 1077041737
13.30429
Norman Luhn
16 Jan 2023
45
21026
 1377972677 1377993703
12.89759
Norman Luhn
16 Jan 2023
46
22080
 1386740653 1386762733
13.53189
Norman Luhn
16 Jan 2023
47
22230
 1508496107 1508518337
13.46171
Norman Luhn
16 Jan 2023
48
24996
 1571442491 1571467487
15.04921
Norman Luhn
16 Jan 2023
49
30636
 3792916031 3792946667
16.32141
Norman Luhn
16 Jan 2023
50
32010
 5557245011 5557277021
16.19726
Norman Luhn
16 Jan 2023
51
34712
 10917979211 10918013923
16.06950
Norman Luhn
16 Jan 2023
52
32882
 11899610141 11899643023
15.05348
Norman Luhn
16 Jan 2023
53
32376
 14743339447 14743371823
14.41859
Norman Luhn
16 Jan 2023
54
37354
 14997196783 14997234137
16.59920
Norman Luhn
16 Jan 2023
55
33786
 19009732597 19009766383
14.56699
Norman Luhn
16 Jan 2023
56
32762
 19164259061 19164291823
14.11101
Norman Luhn
16 Jan 2023
57
34556
 19282830401 19282864957
14.87208
Norman Luhn
16 Jan 2023
58
40640
 32718329867 32718370507
16.36947
Norman Luhn
16 Jan 2023
59
42090
 33429047207 33429089297
16.90845
Norman Luhn
16 Jan 2023
60
41606
 38111128787 38111170393
16.44569
Norman Luhn
16 Jan 2023
61
42602
 44398799741 44398842343
16.52668
Norman Luhn
16 Jan 2023
62
44010
 47006833337 47006877347
16.95419
Norman Luhn
16 Jan 2023
63
45990
 58321920407 58321966397
17.25851
Norman Luhn
16 Jan 2023
64
48176
 105281761811 105281809987
16.84576
Norman Luhn
16 Jan 2023
65
48776
 109004021807 109004070583
16.98571
Norman Luhn
16 Jan 2023
66
49410
 141715121683 141715171093
16.68428
Norman Luhn
16 Jan 2023
67
50336
 144082435241 144082485577
16.96411
Norman Luhn
16 Jan 2023
68
52626
 159383338811 159383391437
17.52851
Norman Luhn
16 Jan 2023
69
53970
 171872741077 171872795047
17.81935
Norman Luhn
16 Jan 2023
70
55680
 223056058787 223056114467
17.83925
Norman Luhn
16 Jan 2023
71
62810
 282040759727 282040822537
19.59114
Norman Luhn
16 Jan 2023
72
66454
 456965055427 456965121881
19.63005
Norman Luhn
16 Jan 2023
73
66610
 817283057737 817283124347
18.45132
Norman Luhn
16 Jan 2023
74
67474
 886834203547 886834271021
18.52468
Norman Luhn
16 Jan 2023
75
68496
 1148501321711 1148501390207
18.28488
Norman Luhn
16 Jan 2023
76
72088
 1214757594103 1214757666191
19.12762
Norman Luhn
16 Jan 2023
77
78054
 1615450122677 1615450200731
20.08691
Norman Luhn
16 Jan 2023
78
78170
 1820832235037 1820832313207
19.86200
Norman Luhn
16 Jan 2023
79
80038
 2276967372283 2276967452321
19.86106
Norman Luhn
17 Jan 2023
80
82414
 2896576381327 2896576463741
19.94035
Norman Luhn
17 Jan 2023
81
82684
 3348266778313 3348266860997
19.70561
Norman Luhn
17 Jan 2023
82
90930
 4600149323597 4600149414527
20.97026
Norman Luhn
17 Jan 2023
83
91116
 5944901308897 5944901400013
20.46831
Norman Luhn
17 Jan 2023
84
91926
 6588388264357 6588388356283
20.43531
Norman Luhn
17 Jan 2023
85
98964
 7164632317723 7164632416687
21.81345
Norman Luhn
17 Jan 2023
86
105490
 14191928461897 14191928567387
21.71274
Norman Luhn
17 Jan 2023
87
108960
 20045661683233 20045661792193
21.67690
Norman Luhn
17 Jan 2023
88
117060
 21235614486127 21235614603187
23.15730
Norman Luhn
17 Jan 2023
89
118744
 38210955295477 38210955414221
22.19144
Norman Luhn
17 Jan 2023
90
121560
 44956566109333 44956566230893
22.36707
Norman Luhn
17 Jan 2023
91
125940
 51812441403911 51812441529851
22.86193
Norman Luhn
17 Jan 2023
92
128760
 57326069354773 57326069483533
23.15073
Norman Luhn
17 Jan 2023
93
144154
 72752877524683 72752877668837
25.34230
Norman Luhn
17 Jan 2023
94
150416
 132752264953307 132752265103723
25.00301
Norman Luhn
20 Jan 2023
95
152496
 145423701927697 145423702080193
25.13675
Norman Luhn
20 Jan 2023
96
161462
 191207198966891 191207199128353
25.95562
Norman Luhn
20 Jan 2023
97
163674
 423897639786343 423897639950017
24.48914
Norman Luhn
21 Jan 2023
98
176274
 429289538789477 429289538965751
26.34470
Norman Luhn
21 Jan 2023
99
182034
 509660461907743 509660462089777
26.79404
Norman Luhn
22 Jan 2023
100
193620
 859879360055687 859879360249307
27.21865
Norman Luhn
23 Jan 2023
Maximal gaps below 1.00 · 1015