Maximal Prime Gaps

Maximal prime gaps are gaps which are larger than all gaps between smaller primes. Gaps with + before the merit also have larger merit than all gaps between smaller primes. merit = size / log(gap start).
Maximal gaps
No Size Gap start Merit Discoverer Year
1 1 P1 = 2 +1.44    
2 2 P1 = 3 +1.82    
3 4 P1 = 7 +2.06    
4 6 P2 = 23 1.91    
5 8 P2 = 89 1.78    
6 14 P3 = 113 +2.96    
7 18 P3 = 523 2.88    
8 20 P3 = 887 2.95    
9 22 P4 = 1129 +3.13    
10 34 P4 = 1327 +4.73    
11 36 P4 = 9551 3.93    
12 44 P5 = 15683 4.55    
13 52 P5 = 19609 +5.26    
14 72 P5 = 31397 +6.95    
15 86 P6 = 155921 +7.19    
16 96 P6 = 360653 +7.50    
17 112 P6 = 370261 +8.74    
18 114 P6 = 492113 8.70    
19 118 P7 = 1349533 8.36    
20 132 P7 = 1357201 +9.35    
21 148 P7 = 2010733 +10.20    
22 154 P7 = 4652353 10.03    
23 180 P8 = 17051707 +10.81 Derrick Henry Lehmer 1957
24 210 P8 = 20831323 +12.46 Derrick Henry Lehmer 1957
25 220 P8 = 47326693 12.45 Kenneth I. Appel & J. Barkley Rosser 1961
26 222 P9 = 122164747 11.92 L. J. Lander & Thomas R. Parkin 1967
27 234 P9 = 189695659 12.28 L. J. Lander & Thomas R. Parkin 1967
28 248 P9 = 191912783 +13.00 L. J. Lander & Thomas R. Parkin 1967
29 250 P9 = 387096133 12.64 L. J. Lander & Thomas R. Parkin 1967
30 282 P9 = 436273009 +14.18 L. J. Lander & Thomas R. Parkin 1967
31 288 P10 = 1294268491 13.73 L. J. Lander & Thomas R. Parkin 1967
32 292 P10 = 1453168141 13.84 L. J. Lander & Thomas R. Parkin 1967
33 320 P10 = 2300942549 +14.84 L. J. Lander & Thomas R. Parkin 1967
34 336 P10 = 3842610773 +15.22 L. J. Lander & Thomas R. Parkin 1967
35 354 P10 = 4302407359 +15.96 L. J. Lander & Thomas R. Parkin 1967
36 382 P11 = 10726904659 +16.54 L. J. Lander & Thomas R. Parkin 1967
37 384 P11 = 20678048297 16.17 Richard P. Brent 1973
38 394 P11 = 22367084959 16.53 Richard P. Brent 1973
39 456 P11 = 25056082087 +19.04 Richard P. Brent 1973
40 464 P11 = 42652618343 18.96 Richard P. Brent 1973
41 468 P12 = 127976334671 18.30 Richard P. Brent 1973
42 474 P12 = 182226896239 18.28 Richard P. Brent 1973
43 486 P12 = 241160624143 18.54 Richard P. Brent 1973
44 490 P12 = 297501075799 18.55 Richard P. Brent 1973
45 500 P12 = 303371455241 18.91 Richard P. Brent 1973
46 514 P12 = 304599508537 +19.44 Richard P. Brent 1973
47 516 P12 = 416608695821 19.29 Richard P. Brent 1973
48 532 P12 = 461690510011 +19.81 Richard P. Brent 1973
49 534 P12 = 614487453523 19.67 Richard P. Brent 1973
50 540 P12 = 738832927927 19.76 Richard P. Brent 1973
51 582 P13 = 1346294310749 +20.84 Richard P. Brent 1973
52 588 P13 = 1408695493609 +21.02 Richard P. Brent 1973
53 602 P13 = 1968188556461 +21.27 Richard P. Brent 1973
54 652 P13 = 2614941710599 +22.80 Richard P. Brent 1973
55 674 P13 = 7177162611713 22.77 Jeff Young & Aaron Potler 1989
56 716 P14 = 13829048559701 +23.66 Jeff Young & Aaron Potler 1989
57 766 P14 = 19581334192423 +25.03 Jeff Young & Aaron Potler 1989
58 778 P14 = 42842283925351 24.79 Jeff Young & Aaron Potler 1989
59 804 P14 = 90874329411493 25.02 Jeff Young & Aaron Potler 1991
60 806 P15 = 171231342420521 24.59 Thomas R. Nicely 1995
61 906 P15 = 218209405436543 +27.44 Thomas R. Nicely 1996
62 916 P16 = 1189459969825483 26.39 Thomas R. Nicely 1998
63 924 P16 = 1686994940955803 26.35 Bertil Nyman 1999
64 1132 P16 = 1693182318746371 +32.28 Bertil Nyman 1999
65 1184 P17 = 43841547845541059 30.90 Bertil Nyman 2002
66 1198 P17 = 55350776431903243 31.07 Tomás Oliveira e Silva 2002
67 1220 P17 = 80873624627234849 31.34 Tomás Oliveira e Silva 2003
68 1224 P18 = 203986478517455989 30.71 Tomás Oliveira e Silva 2005
69 1248 P18 = 218034721194214273 31.26 Tomás Oliveira e Silva 2005
70 1272 P18 = 305405826521087869 31.59 Tomás Oliveira e Silva 2006
71 1328 P18 = 352521223451364323 +32.87 Tomás Oliveira e Silva 2006
72 1356 P18 = 401429925999153707 +33.45 Donald E. Knuth 2006
73 1370 P18 = 418032645936712127 +33.77 Donald E. Knuth 2006
74 1442 P18 = 804212830686677669 +34.98 Siegfried Herzog & Tomás Oliveira e Silva 2005
75 1476 P19 = 1425172824437699411 +35.31 Tomás Oliveira e Silva 2009

The search is exhaustive to 4×1018 as of 30 December 2015.
The Top-20 merits include a few known prime gaps with larger merit than any of the above. They are between far larger primes and extremely unlikely to be maximal gaps. As of 25 August 2016, the largest known merit is:
Size Gap start Merit Discoverer Year
10716 P127 = 7910896513*283#/30 - 6480 36.86     Dana Jacobsen 2016

Made by Jens Kruse Andersen, jens.k.a@get2net.dk   The Top-20 Prime Gaps  home
Data from Thomas R. Nicely's First occurrence prime gaps was used.
Last updated 25 August 2016.