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 |
|
Maximal gaps below 1.845724 · 1019
|
|
Get "The First Occurrence Gap Between Primes"-table
|