Table of Known Maximal Gaps  
(from the Prime Pages' list of frequently asked questions)
 Our book "Prime Curios! The Dictionary of Prime Number Trivia" is now available on CreateSpace, Amazon, ....


Home
Search Site

Largest
The 5000
Top 20
Finding
How Many?
Mersenne

Glossary
Prime Curios!
Prime Lists

FAQ
e-mail list
Titans

Submit primes

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
---- --------------------  ----------------------------
(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>