Table of Known Maximal Gaps

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
1369    418032645936712127  Donald E. Knuth
1441    804212830686677669  Siegfried Herzog & Tomás Oliveira e Silva
1475   1425172824437699411  Tomás Oliveira e Silva
1550  18361375334787046697  Bertil Nyman
---- ---------------------  ----------------------------
(If you know of results beyond those in this table, please let me know.)
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.