Table of Known Maximal Gaps  
(from the Prime Pages' list of frequently asked questions)
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In the following table we list the maximal gaps through 1355.  These are the first occurrences of gaps of at least this length.  For example, there is a gap of 879 composites after the prime

277900416100927.
This is the first occurrence of a gap of this length, but still is not a maximal gap since 905 composites follow the smaller prime
218209405436543.
(These examples are taken from [Nicely99]).  For more information, see page on prime gaps.  See also Nicely's table of prime gaps for a more extensive list which includes all of the known first occurrences of prime gaps--not just the maximal ones.

Warning: there are two standard definitions of "gap".  Let p be a prime and q be the next prime.  Some define the gap between these two primes to be the number of composites between them, so g = q - p - 1 (and the gap following the prime 2 has length 0).  Others define it to be simply q - p (so the gap following the prime 2 has the length 1).  On these pages we use the former definition.  Jens Kruse Andersen's page on maximal gaps and Nicely's pages use the second.

---- -------------------  ----------------------------
gap  following the prime  reference
---- -------------------  ----------------------------
   0                   2
   1                   3
   3                   7
   5                  23
   7                  89
  13                 113
  17                 523
  19                 887
  21                1129
  33                1327
  35                9551
  43               15683
  51               19609
  71               31397
  85              155921
  95              360653
 111              370261
 113              492113
 117             1349533
 131             1357201
 147             2010733
 153             4652353
 179            17051707
 209            20831323
 219            47326693
 221           122164747
 233           189695659
 247           191912783
 249           387096133
 281           436273009
 287          1294268491
 291          1453168141
 319          2300942549
 335          3842610773
 353          4302407359
 381         10726904659
 383         20678048297
 393         22367084959
 455         25056082087
 463         42652618343
 467        127976334671
 473        182226896239
 485        241160624143
 489        297501075799
 499        303371455241
 513        304599508537
 515        416608695821
 531        461690510011
 533        614487453523
 539        738832927927
 581       1346294310749
 587       1408695493609
 601       1968188556461
 651       2614941710599
 673       7177162611713
 715      13829048559701  [YP89]
 765      19581334192423  [YP89]
 777      42842283925351  [YP89]
 803      90874329411493  [Nicely99]
 805     171231342420521  [Nicely99]
 905     218209405436543  [Nicely99]
 915    1189459969825483  [NN99]
 923    1686994940955803  [NN99]
1131    1693182318746371  [NN99]
1183   43841547845541059  [NN2002]
1197   55350776431903243  Tomás Oliveira e Silva
1219   80873624627234849  Tomás Oliveira e Silva
1223 203986478517455989 Tomás Oliveira e Silva 1247 218034721194214273 Tomás Oliveira e Silva 1271 305405826521087869 Tomás Oliveira e Silva 1327 352521223451364323 Tomás Oliveira e Silva 1355 401429925999153707 Donald E. Knuth ---- ------------------- ----------------------------
(If you know of results beyond those in this table, please let me know.)
The Prime Pages
Another prime page by Chris K. Caldwell <caldwell@utm.edu>