%N Distinct even prime-gap lengths (number of composites between primes), from 3+2, 7+4, 23+6,...
%C Nicely and Nyman have sieved up to 1.3565*10^16 at least. They admit it is likely they have suffered from hardware or software bugs, but believe the probability the sequence up to this point is incorrect is <1 in a million. This sequence is presumably all even integers (in different order). It is not monotonic. The monotonic subsequence of record-breaking prime gaps is A005250.
%C Essentially the same as A014320. [From _R. J. Mathar_, Oct 13 2008]
%H Richard P. Brent, <a href="http://dx.doi.org/10.1090/S0025-5718-1973-0330021-0">The first occurrence of large gaps between successive primes</a>, Math. Comp. 27:124 (1973), 959-963.
%H T. R. Nicely, <a href="http://dx.doi.org/10.1090/S0025-5718-99-01065-0">New maximal prime gaps and first occurrences</a>, Math. Comput. 68,227 (1999) 1311-1315.
%H T. R. Nicely, <a href="http://www.trnicely.net/gaps/gaplist.html">List of prime gaps</a>
%t DeleteDuplicates[Differences[Prime[Range[2,200000]]]] (* _Harvey P. Dale_, Dec 07 2014 *)
%Y Cf. A008996, A005250.
%Y Equals 2*A014321(n-1).
%A _Warren D. Smith_, Dec 11 2000
%E Comment corrected by _Harvey P. Dale_, Dec 07 2014