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 on 23 February 2012.
There is a single known prime gap with larger merit than any of the above. It is between far larger primes and is extremely unlikely to be a maximal gap:
Size Gap start Merit Discoverer Year
66520 P816 = 1931*1933#/7230 - 30244 35.42 Michiel Jansen 2012

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 24 February 2012.