Table of Known Maximal Gaps
By Chris Caldwell, et al.
In the following table we list the maximal gaps through 1853. 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 (archive.org) for a more extensive list which includes all of the known first occurrences of prime gaps — not just the maximal ones, as well as a community project which has been maintaining the list since the death of Dr. Nicely in 2019.
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 1487 5733241593241196731 Anand S. Nair 1509 6787988999657777797 1525 15570628755536096243 1529 17678654157568189057 Bertil Nyman 1549 18361375334787046697 Bertil Nyman 1551 18470057946260698231 Craig Loizides 1571 18571673432051830099 Craig Loizides 1675 20733746510561442863 Brian Kehrig 1723 68068810283234182907 Martin Raab & Brian Kehrig 1853 101412319996363309069 Robert Smith & Brian Kehrig ---- ---------------------- ----------------------------(If you know of results beyond those in this table, please let us know.)