This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A317479 #9 Aug 19 2018 18:14:03
%S A317479 2,3,5,7,11,23,29,31,41,47,61,79,83,101,137,193,199,337,349,557,677,
%T A317479 977,1069,1087,1279,1483,1579,1877,2053,2591,2713,2843,3359,3823,4243,
%U A317479 6011,7393,7411,7459,8179,8389,15313,18287,19463,21323,22153,23011,27067
%N A317479 Primes with record values of corresponding Fortunate numbers (A005235).
%C A317479 The corresponding record values of the Fortunate numbers are 3, 5, 7, 13, 23, 37, 61, 67, 71, 107, 109, 151, 197, 233, 643, 751, 773, 883, 1381, 1423, 2087, 2243, 2357, 3559, 3739, 5323, 5689, 6271, 7187, 7309, 8713, 11069, 11411, 19699, 20249, 25621, 28351, 28817, 32443, 39769, 59981, 78059, 82339, 86293, 89657, 90127, 101021, 129589, ...
%C A317479 Primes that are in both of these 2 sequences: 3, 5, 7, 23, 61, ...
%e A317479 23 is in the sequence since the prime next to 23#+1 is 23#+37 and 37 is larger than all the Fortunate numbers before it (3, 5, 7, 13, 23, 17, 19, 23).
%t A317479 primorial[n_] := Times @@ Prime[Range[n]]; gap[n_] := NextPrime[n + 1] - n; fort[n_] := gap[primorial[n]]; fm=0; s={}; Do[f = fort[n]; If[f > fm, AppendTo[s, Prime[n]]; fm = f], {n, 1, 30}]; s
%Y A317479 Cf. A005235.
%K A317479 nonn
%O A317479 1,1
%A A317479 _Amiram Eldar_, Jul 29 2018