←
Record Gaps Between Primes

Reference:OEIS A002386

Gap end
merit = ∫dt / log t
Gap start
Rank Gap Size Gap start Next Prime Merit Who When
1 1 2 3 1.442695 Euclid 300 B.C.
2 2 3 5 1.820478 A. E. Western 1934
3 4 7 11 2.055593 J. W. L. Glaisher 1877
4 6 23 29 1.913573 J. W. L. Glaisher 1877
5 8 89 97 1.782278 J. W. L. Glaisher 1877
6 14 113 127 2.961466 J. W. L. Glaisher 1877
7 18 523 541 2.875591 J. W. L. Glaisher 1877
8 20 887 907 2.946443 J. W. L. Glaisher 1877
9 22 1129 1151 3.129851 A. E. Western 1934
10 34 1327 1361 4.728345 J. W. L. Glaisher 1877
11 36 9551 9587 3.928243 J. W. L. Glaisher 1877
12 44 15683 15727 4.554708 J. W. L. Glaisher 1877
13 52 19609 19661 5.261164 J. W. L. Glaisher 1877
14 72 31397 31469 6.953520 J. W. L. Glaisher 1877
15 86 155921 156007 7.192376 J. W. L. Glaisher 1877
16 96 360653 360749 7.502537 Derrick Henry Lehmer 1957
17 112 370261 370373 8.735011 J. W. L. Glaisher 1877
18 114 492113 492227 8.697998 J. W. L. Glaisher 1877
19 118 1349533 1349651 8.359741 J. W. L. Glaisher 1877
20 132 1357201 1357333 9.347822 J. W. L. Glaisher 1877
21 148 2010733 2010881 10.19704 J. W. L. Glaisher 1877
22 154 4652353 4652507 10.03068 A. E. Western 1934
23 180 17051707 17051887 10.80966 Derrick Henry Lehmer 1957
24 210 20831323 20831533 12.46145 Derrick Henry Lehmer 1957
25 220 47326693 47326913 12.44865 Gruenberger et.al, Appel and Rosser 1961
26 222 122164747 122164969 11.92209 Lander and Parkin 1967
27 234 189695659 189695893 12.27641 Lander and Parkin 1967
28 248 191912783 191913031 13.00297 Lander and Parkin 1967
29 250 387096133 387096383 12.64274 Lander and Parkin 1967
30 282 436273009 436273291 14.17528 Lander and Parkin 1967
31 288 1294268491 1294268779 13.72656 Lander and Parkin 1967
32 292 1453168141 1453168433 13.84082 Lander and Parkin 1967
33 320 2300942549 2300942869 14.84465 Lander and Parkin 1967
34 336 3842610773 3842611109 15.22468 Lander and Parkin 1967
35 354 4302407359 4302407713 15.95856 Lander and Parkin 1967
36 382 10726904659 10726905041 16.53964 Lander and Parkin 1967
37 384 20678048297 20678048681 16.16682 Richard P. Brent 1973
38 394 22367084959 22367085353 16.53318 Richard P. Brent 1973
39 456 25056082087 25056082543 19.04413 Richard P. Brent 1973
40 464 42652618343 42652618807 18.95707 Richard P. Brent 1973
41 468 127976334671 127976335139 18.29904 Richard P. Brent 1973
42 474 182226896239 182226896713 18.28102 Richard P. Brent 1973
43 486 241160624143 241160624629 18.54344 Richard P. Brent 1973
44 490 297501075799 297501076289 18.54747 Richard P. Brent 1973
45 500 303371455241 303371455741 18.91201 Richard P. Brent 1973
46 514 304599508537 304599509051 19.43857 Richard P. Brent 1973
47 516 416608695821 416608696337 19.28581 Richard P. Brent 1973
48 532 461690510011 461690510543 19.80776 Richard P. Brent 1973
49 534 614487453523 614487454057 19.67281 Richard P. Brent 1973
50 540 738832927927 738832928467 19.75970 Richard P. Brent 1973
51 582 1346294310749 1346294311331 20.83901 Richard P. Brent 1973
52 588 1408695493609 1408695494197 21.01975 Richard P. Brent 1973
53 602 1968188556461 1968188557063 21.26597 Richard P. Brent 1973
54 652 2614941710599 2614941711251 22.80337 Richard P. Brent 1973
55 674 7177162611713 7177162612387 22.76878 Jeff Young and Aaron Potler 1989
56 716 13829048559701 13829048560417 23.66332 Jeff Young and Aaron Potler 1989
57 766 19581334192423 19581334193189 25.02810 Jeff Young and Aaron Potler 1989
58 778 42842283925351 42842283926129 24.78611 Jeff Young and Aaron Potler 1989
59 804 90874329411493 90874329412297 25.01516 Jeff Young and Aaron Potler, [by Paulo Ribenboim] 1991
60 806 171231342420521 171231342421327 24.59263 Thomas R. Nicely 1995
61 906 218209405436543 218209405437449 27.44084 Thomas R. Nicely 1996
62 916 1189459969825483 1189459969826399 26.38835 Thomas R. Nicely 1998
63 924 1686994940955803 1686994940956727 26.35352 Bertil Nyman 1999
64 1132 1693182318746371 1693182318747503 32.28254 Bertil Nyman 1999
65 1184 43841547845541059 43841547845542243 30.89822 Bertil Nyman 2002
66 1198 55350776431903243 55350776431904441 31.07453 Tomás Oliveira e Silva 2002
67 1220 80873624627234849 80873624627236069 31.33695 Tomás Oliveira e Silva 2003
68 1224 203986478517455989 203986478517457213 30.70991 Tomás Oliveira e Silva 2005
69 1248 218034721194214273 218034721194215521 31.25983 Tomás Oliveira e Silva 2005
70 1272 305405826521087869 305405826521089141 31.59430 Tomás Oliveira e Silva 2006
71 1328 352521223451364323 352521223451365651 32.86812 Tomás Oliveira e Silva 2006
72 1356 401429925999153707 401429925999155063 33.45355 Donald Ervin Knuth 2006
73 1370 418032645936712127 418032645936713497 33.76518 Donald Ervin Knuth 2006
74 1442 804212830686677669 804212830686679111 34.97568 Siegfried “Zig” Herzog, [Tomás Oliveira e Silva] 2005
75 1476 1425172824437699411 1425172824437700887
35.31030
 Tomás Oliveira e Silva 2009
76 1488 5733241593241196731 5733241593241198219 34.45017 Anand S. Nair 2017
77 1510 6787988999657777797 6787988999657779307 34.82336 Dana Jacobsen 2017
78 1526 15570628755536096243 15570628755536097769 34.53120 Steve Cole 2018
79 1530 17678654157568189057 17678654157568190587 34.52252 Bertil Nyman 2014
80 1550 18361375334787046697 18361375334787048247 34.94392 Bertil Nyman 2014
81 1552 18470057946260698231 18470057946260699783 34.98436 Craig Loizides (Verification 30 Dec 2023) 2021
Maximal gaps below 1.8486 · 1019 → ( 264 + 39,255,926,290,448,384 )
Get "The First Occurrence Gap Between Primes"-table