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 8.306282 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 4492102614469661 4492102614902261 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 37354 14997196783 14997234137 16.59920 Norman Luhn 16 Jan 2023
53 40640 32718329867 32718370507 16.36947 Norman Luhn 16 Jan 2023
54 42090 33429047207 33429089297 16.90845 Norman Luhn 16 Jan 2023
55 42602 44398799741 44398842343 16.52668 Norman Luhn 16 Jan 2023
56 44010 47006833337 47006877347 16.95419 Norman Luhn 16 Jan 2023
57 45990 58321920407 58321966397 17.25851 Norman Luhn 16 Jan 2023
58 48176 105281761811 105281809987 16.84576 Norman Luhn 16 Jan 2023
59 48776 109004021807 109004070583 16.98571 Norman Luhn 16 Jan 2023
60 49410 141715121683 141715171093 16.68428 Norman Luhn 16 Jan 2023
61 50336 144082435241 144082485577 16.96411 Norman Luhn 16 Jan 2023
62 52626 159383338811 159383391437 17.52851 Norman Luhn 16 Jan 2023
63 53970 171872741077 171872795047 17.81935 Norman Luhn 16 Jan 2023
64 55680 223056058787 223056114467 17.83925 Norman Luhn 16 Jan 2023
65 62810 282040759727 282040822537 19.59114 Norman Luhn 16 Jan 2023
66 66454 456965055427 456965121881 19.63005 Norman Luhn 16 Jan 2023
67 66610 817283057737 817283124347 18.45132 Norman Luhn 16 Jan 2023
68 67474 886834203547 886834271021 18.52468 Norman Luhn 16 Jan 2023
69 68496 1148501321711 1148501390207 18.28488 Norman Luhn 16 Jan 2023
70 72088 1214757594103 1214757666191 19.12762 Norman Luhn 16 Jan 2023
71 78054 1615450122677 1615450200731 20.08691 Norman Luhn 16 Jan 2023
72 78170 1820832235037 1820832313207 19.86200 Norman Luhn 16 Jan 2023
73 80038 2276967372283 2276967452321 19.86106 Norman Luhn 17 Jan 2023
74 82414 2896576381327 2896576463741 19.94035 Norman Luhn 17 Jan 2023
75 82684 3348266778313 3348266860997 19.70561 Norman Luhn 17 Jan 2023
76 90930 4600149323597 4600149414527 20.97026 Norman Luhn 17 Jan 2023
77 91116 5944901308897 5944901400013 20.46831 Norman Luhn 17 Jan 2023
78 91926 6588388264357 6588388356283 20.43531 Norman Luhn 17 Jan 2023
79 98964 7164632317723 7164632416687 21.81345 Norman Luhn 17 Jan 2023
80 105490 14191928461897 14191928567387 21.71274 Norman Luhn 17 Jan 2023
81 108960 20045661683233 20045661792193 21.67690 Norman Luhn 17 Jan 2023
82 117060 21235614486127 21235614603187 23.15730 Norman Luhn 17 Jan 2023
83 118744 38210955295477 38210955414221 22.19144 Norman Luhn 17 Jan 2023
84 121560 44956566109333 44956566230893 22.36707 Norman Luhn 17 Jan 2023
85 125940 51812441403911 51812441529851 22.86193 Norman Luhn 17 Jan 2023
86 128760 57326069354773 57326069483533 23.15073 Norman Luhn 17 Jan 2023
87 144154 72752877524683 72752877668837 25.34230 Norman Luhn 17 Jan 2023
88 150416 132752264953307 132752265103723 25.00301 Norman Luhn 20 Jan 2023
89 152496 145423701927697 145423702080193 25.13675 Norman Luhn 20 Jan 2023
90 161462 191207198966891 191207199128353 25.95562 Norman Luhn 20 Jan 2023
91 163674 423897639786343 423897639950017 24.48914 Norman Luhn 21 Jan 2023
92 176274 429289538789477 429289538965751 26.34470 Norman Luhn 21 Jan 2023
93 182034 509660461907743 509660462089777 26.79404 Norman Luhn 22 Jan 2023
94 193620 859879360055687 859879360249307
27.21865
Norman Luhn 23 Jan 2023
Maximal gaps below 1.00 · 1015