Record Gaps Between Prime Quintuplets

References: OEIS A201073 & OEIS A201062

Pattern d: d = 0, 2, 6, 8, 12
Gap end
merit = 10.1317949 ·dt / log5 t
Gap start
Rank Gap Size Gap start Next Prime Quintuplet Merit Who When
1 6 5 11 2.014091 Alexei Kourbatov 2013
2 90 11 101 1.615652 Alexei Kourbatov 2013
3 1380 101 1481 1.475054 Alexei Kourbatov 2013
4 14580 1481 16061 2.821400 Alexei Kourbatov 2013
5 21510 22271 43781 1.812143 Alexei Kourbatov 2013
6 88830 55331 144161 4.561779 Alexei Kourbatov 2013
7 97020 536441 633461 2.382030 Alexei Kourbatov 2013
8 107100 661091 768191 2.439605 Alexei Kourbatov 2013
9 112140 1461401 1573541 1.945726 Alexei Kourbatov 2013
10 301890 1615841 1917731 4.969311 Alexei Kourbatov 2013
11 401820 5527001 5928821 4.462615 Alexei Kourbatov 2013
12 577710 11086841 11664551 5.170724 Alexei Kourbatov 2013
13 689850 35240321 35930171 4.398101 Alexei Kourbatov 2013
14 846210 53266391 54112601 4.799780 Alexei Kourbatov 2013
15 857010 72610121 73467131 4.461704 Alexei Kourbatov 2013
16 986160 92202821 93188981 4.809118 Alexei Kourbatov 2013
17 1655130 117458981 119114111 7.555860 Alexei Kourbatov 2013
18 2035740 196091171 198126911 8.115696 Alexei Kourbatov 2013
19 2266320 636118781 638385101 6.705826 Alexei Kourbatov 2013
20 2467290 975348161 977815451 6.578094 Alexei Kourbatov 2013
21 2614710 1156096301 1158711011 6.691992 Alexei Kourbatov 2013
22 3305310 1277816921 1281122231 8.259169 Alexei Kourbatov 2013
23 3530220 1347962381 1351492601 8.709582 Alexei Kourbatov 2013
24 3880050 2195593481 2199473531 8.536129 Alexei Kourbatov 2013
25 3885420 3128295551 3132180971 7.878418 Alexei Kourbatov 2013
26 5290440 4015046591 4020337031 10.13547 Alexei Kourbatov 2013
27 5713800 8280668651 8286382451 9.318915 Alexei Kourbatov 2013
28 6049890 9027127091 9033176981 9.682723 Alexei Kourbatov 2013
29 6128340 15686967971 15693096311 8.707265 Alexei Kourbatov 2013
30 7949040 18901038971 18908988011 10.85626 Alexei Kourbatov 2013
31 7971270 21785624291 21793595561 10.56575 Alexei Kourbatov 2013
32 10770150 30310287431 30321057581 13.32532 Alexei Kourbatov 2013
33 11340840 107604759671 107616100511 10.86452 Alexei Kourbatov 2013
34 12249510 140760439991 140772689501 11.13382 Alexei Kourbatov 2013
35 12413190 162661360481 162673773671 10.97012 Alexei Kourbatov 2013
36 14181000 187735329491 187749510491 12.19014 Alexei Kourbatov 2013
37 16092930 327978626531 327994719461 12.43832 Alexei Kourbatov 2013
38 16360350 508259311991 508275672341 11.65040 Alexei Kourbatov 2013
39 16756740 620537349191 620554105931 11.50052 Alexei Kourbatov 2013
40 16981320 667672901711 667689883031 11.49880 Alexei Kourbatov 2013
41 17590230 1079628551621 1079646141851 10.91339 Alexei Kourbatov 2013
42 19285140 1104604933841 1104624218981 11.91569 Alexei Kourbatov 2013
43 19525590 1182148717481 1182168243071 11.91775 Alexei Kourbatov 2013
44 22230180 1197151034531 1197173264711 13.53780 Alexei Kourbatov 2013
45 22549470 2286697462781 2286720012251 12.24026 Alexei Kourbatov 2013
46 29986530 2435950632251 2435980618781 16.09760 Alexei Kourbatov 2013
47 32168520 3276773115431 3276805283951 16.39860 Alexei Kourbatov 2013
48 36392070 5229301162991 5229337555061 17.11766 Alexei Kourbatov 2013
49 38695230 9196865051651 9196903746881 16.54361 Alexei Kourbatov 2013
50 40156200 14660925945221 14660966101421 15.88783 Alexei Kourbatov 2013
51 40618500 21006417451961 21006458070461 15.15051 Alexei Kourbatov 2013
52 40996500 22175175736991 22175216733491 15.15726 Alexei Kourbatov 2013
53 41452320 22726966063091 22727007515411 15.26464 Alexei Kourbatov 2013
54 47578140 22931291089451 22931338667591 17.49498 Alexei Kourbatov 2013
55 48630870 31060723328351 31060771959221 17.02567 Alexei Kourbatov 2013
56 55044570 85489258071311 85489313115881 16.41605 Alexei Kourbatov 2013
57 58465680 90913430825291 90913489290971 17.27011 Alexei Kourbatov 2013
58 65048220 96730325054171 96730390102391 19.03021 Alexei Kourbatov 2013
59 65737980 199672700175071 199672765913051 17.20662 Alexei Kourbatov 2013
60 70788900 275444947505591 275445018294491 17.64948 Alexei Kourbatov 2013
61 73970820 331992774272981 331992848243801 17.93356 Alexei Kourbatov 2013
62 79985130 465968834865971 465968914851101 18.43783 Alexei Kourbatov 2013
63 82420290 686535413263871 686535495684161 17.94572 Alexei Kourbatov 2013
64 88092570 761914822198961 761914910291531 18.89097 Alexei Kourbatov 2013
65 89780040 1144708485094541 1144708574874581 18.14893 Norman Luhn 11 Nov 2022
66 89999700 1151759067731681 1151759157731381 18.17723 Norman Luhn 11 Nov 2022
67 92278290 1652750938094561 1652751030372851 17.69660 Norman Luhn 11 Nov 2022
68 96260340 2738101496927891 2738101593188231 17.18611 Norman Luhn 11 Nov 2022
69 106240140 2783651538720581 2783651644960721 18.92392 Norman Luhn 11 Nov 2022
70 109965150 2791544717194061 2791544827159211 19.57964 Norman Luhn 11 Nov 2022
71 113717100 3943459477670891 3943459591387991 19.29233 Norman Luhn 12 Nov 2022
72 125811090 4323771559383161 4323771685194251
21.07258
Norman Luhn 12 Nov 2022
73 131738370 6044436969077321 6044437100815691 21.06681 Norman Luhn 13 Nov 2022
Maximal gaps below 1.00 · 1016

Pattern d: d = 0, 4, 6, 10, 12
Gap end
merit = 10.1317949 ·dt / log5 t
Gap start
Rank Gap Size Gap start Next Prime Quintuplet Merit Who When
1 90 7 97 2.447286 Alexei Kourbatov 2013
2 1770 97 1867 1.668845 Alexei Kourbatov 2013
3 2190 3457 5647 0.528546 Alexei Kourbatov 2013
4 10080 5647 15727 1.541767 Alexei Kourbatov 2013
5 24360 19417 43777 2.109313 Alexei Kourbatov 2013
6 35910 43777 79687 2.250890 Alexei Kourbatov 2013
7 156750 101107 257857 6.260574 Alexei Kourbatov 2013
8 208620 1621717 1830337 3.460981 Alexei Kourbatov 2013
9 304920 3690517 3995437 3.856354 Alexei Kourbatov 2013
10 306390 5425747 5732137 3.431607 Alexei Kourbatov 2013
11 328020 8799607 9127627 3.160959 Alexei Kourbatov 2013
12 422190 9511417 9933607 3.966749 Alexei Kourbatov 2013
13 526350 16388917 16915267 4.195292 Alexei Kourbatov 2013
14 639330 22678417 23317747 4.628609 Alexei Kourbatov 2013
15 706860 31875577 32582437 4.637159 Alexei Kourbatov 2013
16 866460 37162117 38028577 5.437616 Alexei Kourbatov 2013
17 1030770 64210117 65240887 5.549032 Alexei Kourbatov 2013
18 1111620 119732017 120843637 5.051827 Alexei Kourbatov 2013
19 1147440 200271517 201418957 4.551967 Alexei Kourbatov 2013
20 1151100 203169007 204320107 4.549408 Alexei Kourbatov 2013
21 1447530 241307107 242754637 5.470321 Alexei Kourbatov 2013
22 1769670 342235627 344005297 6.114615 Alexei Kourbatov 2013
23 1793070 367358347 369151417 6.085234 Alexei Kourbatov 2013
24 2024610 378200227 380224837 6.820180 Alexei Kourbatov 2013
25 2320170 438140947 440461117 7.531215 Alexei Kourbatov 2013
26 2335080 446609407 448944487 7.543325 Alexei Kourbatov 2013
27 2403570 711616897 714020467 6.918590 Alexei Kourbatov 2013
28 3558030 966813007 970371037 9.504986 Alexei Kourbatov 2013
29 4195500 2044014607 2048210107 9.384832 Alexei Kourbatov 2013
30 4463130 3510456787 3514919917 8.815000 Alexei Kourbatov 2013
31 4602360 4700738167 4705340527 8.509854 Alexei Kourbatov 2013
32 5210190 5798359657 5803569847 9.192503 Alexei Kourbatov 2013
33 5331060 7896734467 7902065527 8.785638 Alexei Kourbatov 2013
34 5368530 12654304207 12659672737 7.986482 Alexei Kourbatov 2013
35 5546520 13890542377 13896088897 8.087940 Alexei Kourbatov 2013
36 5966220 14662830817 14668797037 8.599858 Alexei Kourbatov 2013
37 6557670 15434185927 15440743597 9.349536 Alexei Kourbatov 2013
38 6590640 17375054227 17381644867 9.162921 Alexei Kourbatov 2013
39 7359450 17537596327 17544955777 10.21156 Alexei Kourbatov 2013
40 8673840 25988605537 25997279377 11.08034 Alexei Kourbatov 2013
41 9334500 66407160637 66416495137 9.842651 Alexei Kourbatov 2013
42 9570330 74862035617 74871605947 9.852137 Alexei Kourbatov 2013
43 12983670 77710388047 77723371717 13.26671 Alexei Kourbatov 2013
44 14597820 144124106167 144138703987 13.20737 Alexei Kourbatov 2013
45 16396710 210222262087 210238658797 13.79162 Alexei Kourbatov 2013
46 17639070 585234882097 585252521167 12.23750 Alexei Kourbatov 2013
47 18803070 926017532047 926036335117 11.99440 Alexei Kourbatov 2013
48 23392830 986089952917 986113345747 14.75314 Alexei Kourbatov 2013
49 24122280 2819808136417 2819832258697 12.62237 Alexei Kourbatov 2013
50 26753370 3013422626107 3013449379477 13.83811 Alexei Kourbatov 2013
51 26870130 3538026326827 3538053196957 13.51678 Alexei Kourbatov 2013
52 27378120 4674635167747 4674662545867 13.12718 Alexei Kourbatov 2013
53 28837200 5757142722757 5757171559957 13.34358 Alexei Kourbatov 2013
54 30726150 7464931087717 7464961813867 13.60544 Alexei Kourbatov 2013
55 33297270 8402871269197 8402904566467 14.45306 Alexei Kourbatov 2013
56 33489540 9292699799017 9292733288557 14.29316 Alexei Kourbatov 2013
57 33619740 10985205390997 10985239010737 13.95339 Alexei Kourbatov 2013
58 36586110 12992848206847 12992884792957 14.76716 Alexei Kourbatov 2013
59 42483960 15589051692667 15589094176627 16.63967 Alexei Kourbatov 2013
60 44167530 24096376903597 24096421071127 16.11067 Alexei Kourbatov 2013
61 44771370 37371241083097 37371285854467 15.21609 Alexei Kourbatov 2013
62 58972920 38728669335607 38728728308527 19.92864 Alexei Kourbatov 2013
63 67170090 91572717670537 91572784840627 19.81901 Alexei Kourbatov 2013
64 69538470 109950817237357 109950886775827 19.94399 Alexei Kourbatov 2013
65 72542190 325554440818297 325554513360487 17.63879 Alexei Kourbatov 2013
66 73032960 481567288596127 481567361629087 16.75342 Alexei Kourbatov 2013
67 74101230 501796510663237 501796584764467 16.89541 Alexei Kourbatov 2013
68 76243980 535243109721577 535243185965557 17.21921 Alexei Kourbatov 2013
69 78597210 657351798174427 657351876771637 17.22252 Alexei Kourbatov 2013
70 86266530 818872754682547 818872840949077 18.30600 Alexei Kourbatov 2013
71 107597490 991851356676277 991851464273767
22.20589
Alexei Kourbatov 2013
72 112167180 7836574258165897 7836574370333077 17.30974 Norman Luhn 23 Nov 2022
73 113994300 8140099858614037 8140099972608337 17.50065 Norman Luhn 23 Nov 2022
74 123697560 8232448271331367 8232448395028927 18.96111 Norman Luhn 23 Nov 2022
Maximal gaps below 1.00 · 1016


Record Gaps Between Prime Quintuplets Over All Patterns


Gap end
merit = 20.2635899 ·dt / log5 t
Gap start
Rank Gap Size Gap start Next Prime Quintuplet Merit Who When
1 2 5 7 2.325345 Norman Luhn 17 Jan 2023
2 4 7 11 1.702838 Norman Luhn 17 Jan 2023
3 86 11 97 3.191734 Norman Luhn 17 Jan 2023
4 1380 101 1481 2.950108 Norman Luhn 17 Jan 2023
5 1590 1867 3457 1.074268 Norman Luhn 17 Jan 2023
6 2190 3457 5647 1.057092 Norman Luhn 17 Jan 2023
7 10080 5647 15727 3.083535 Norman Luhn 17 Jan 2023
8 21506 22271 43777 3.623705 Norman Luhn 17 Jan 2023
9 24356 55331 79687 2.913718 Norman Luhn 17 Jan 2023
10 43054 101107 144161 3.963805 Norman Luhn 17 Jan 2023
11 48724 470077 518801 2.548873 Norman Luhn 17 Jan 2023
12 90176 536441 626617 4.437438 Norman Luhn 17 Jan 2023
13 208620 1621717 1830337 6.921963 Norman Luhn 17 Jan 2023
14 296520 9627461 9923981 5.562460 Norman Luhn 17 Jan 2023
15 403530 17958757 18362287 6.267510 Norman Luhn 17 Jan 2023
16 415594 37162117 37577711 5.225229 Norman Luhn 17 Jan 2023
17 449104 49682617 50131721 5.200557 Norman Luhn 17 Jan 2023
18 680524 53432077 54112601 7.716635 Norman Luhn 17 Jan 2023
19 818580 134702797 135521377 7.212090 Norman Luhn 17 Jan 2023
20 937024 197189887 198126911 7.465643 Norman Luhn 17 Jan 2023
21 976170 373604711 374580881 6.599401 Norman Luhn 17 Jan 2023
22 977970 493287161 494265131 6.165704 Norman Luhn 17 Jan 2023
23 1034284 637350817 638385101 6.119238 Norman Luhn 17 Jan 2023
24 1091670 712555001 713646671 6.284055 Norman Luhn 17 Jan 2023
25 1359544 860705887 862065431 7.473265 Norman Luhn 17 Jan 2023
26 1395450 1009180807 1010576257 7.380909 Norman Luhn 17 Jan 2023
27 1626454 1157084557 1158711011 8.324521 Norman Luhn 17 Jan 2023
28 1924226 1389333221 1391257447 9.428118 Norman Luhn 17 Jan 2023
29 2203860 3194724097 3196927957 8.895217 Norman Luhn 17 Jan 2023
30 2354396 4380061991 4382416387 8.846522 Norman Luhn 17 Jan 2023
31 2934034 6265437247 6268371281 10.17714 Norman Luhn 17 Jan 2023
32 3405240 8716936927 8720342167 10.98387 Norman Luhn 17 Jan 2023
33 4144050 9027682837 9031826887 13.26505 Norman Luhn 17 Jan 2023
34 4612650 25746845471 25751458121 11.80798 Norman Luhn 17 Jan 2023
35 4694040 27095815927 27100509967 11.88916 Norman Luhn 17 Jan 2023
36 4770026 57004580441 57009350467 10.37335 Norman Luhn 17 Jan 2023
37 6252450 64749989531 64756241981 13.25276 Norman Luhn 17 Jan 2023
38 6281974 125461072567 125467354541 11.67908 Norman Luhn 17 Jan 2023
39 6671400 140763439507 140770110907 12.12753 Norman Luhn 17 Jan 2023
40 6745830 217403883371 217410629201 11.27535 Norman Luhn 17 Jan 2023
41 6969390 219466456207 219473425597 11.62797 Norman Luhn 17 Jan 2023
42 7032810 254585915951 254592948761 11.40592 Norman Luhn 17 Jan 2023
43 7697040 259545134411 259552831451 12.43742 Norman Luhn 17 Jan 2023
44 8009910 267613646467 267621656377 12.86786 Norman Luhn 17 Jan 2023
45 8632800 323447704751 323456337551 13.37977 Norman Luhn 17 Jan 2023
46 9352856 416795008571 416804361427 13.82181 Norman Luhn 17 Jan 2023
47 11596620 496350264491 496361861111 16.58902 Norman Luhn 17 Jan 2023
48 12356190 1722002217907 1722014574097 14.10324 Norman Luhn 17 Jan 2023
49 12414146 2247007282901 2247019697047 13.51878 Norman Luhn 17 Jan 2023
50 12635700 2440461612221 2440474247921 13.56199 Norman Luhn 17 Jan 2023
51 12828270 2817723775117 2817736603387 13.42693 Norman Luhn 17 Jan 2023
52 14258580 3099650725597 3099664984177 14.67822 Norman Luhn 17 Jan 2023
53 14490626 3302152083611 3302166574237 14.75407 Norman Luhn 17 Jan 2023
54 15047344 3590553662947 3590568710291 15.10031 Norman Luhn 17 Jan 2023
55 18575340 3971417681677 3971436257017 18.31907 Norman Luhn 17 Jan 2023
56 19136966 11271950385581 11271969522547 15.81706 Norman Luhn 17 Jan 2023
57 20070120 11626054158281 11626074228401 16.50322 Norman Luhn 17 Jan 2023
58 21305516 13968495046601 13968516352117 16.99426 Norman Luhn 17 Jan 2023
59 24819274 15722575542757 15722600362031 19.41463 Norman Luhn 17 Jan 2023
60 26535600 55267748077897 55267774613497 16.94894 Norman Luhn 17 Jan 2023
61 26866860 101916005765921 101916032632781 15.59324 Norman Luhn 19 Jan 2023
62 26963876 120618225533411 120618252497287 15.24716 Norman Luhn 19 Jan 2023
63 28451606 120632651965361 120632680416967 16.08812 Norman Luhn 19 Jan 2023
64 28761814 139357211063167 139357239824981 15.90644 Norman Luhn 19 Jan 2023
65 29069246 146710464482501 146710493551747 15.95015 Norman Luhn 19 Jan 2023
66 29348460 152377895932391 152377925280851 16.01012 Norman Luhn 19 Jan 2023
67 31270804 153561290445457 153561321716261 17.03860 Norman Luhn 19 Jan 2023
68 32676720 174263039990857 174263072667577 17.46395 Norman Luhn 19 Jan 2023
69 34005810 193262636332387 193262670338197 17.89020 Norman Luhn 19 Jan 2023
70 39872876 239249216549501 239249256422377 20.30928 Norman Luhn 19 Jan 2023
71 40033140 414088181123621 414088221156761 18.78246 Norman Luhn 19 Jan 2023
72 46997490 555818816805607 555818863803097 21.11050 Norman Luhn 19 Jan 2023
73 52505970 932750269787377 932750322293347
21.86612
Norman Luhn 20 Jan 2023
Maximal gaps below 1.00 · 1015