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%I #13 Oct 28 2021 13:06:09
%S 2,4,6,8,14,10,12,18,20,22,34,24,16,26,28,30,32,36,44,42,40,52,48,38,
%T 72,50,62,54,60,58,46,56,64,68,86,66,70,78,76,82,96,112,100,74,90,84,
%U 114,80,88,98,92,106,94,118,132,104,102,110,126,120,148,108
%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 Thomas 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 Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]
%t DeleteDuplicates[Differences[Prime[Range[2,200000]]]] (* _Harvey P. Dale_, Dec 07 2014 *)
%Y Cf. A008996, A005250.
%Y Equals 2*A014321(n-1).
%K hard,nice,nonn
%O 0,1
%A _Warren D. Smith_, Dec 11 2000
%E Comment corrected by _Harvey P. Dale_, Dec 07 2014
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