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.
