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 A124147 #18 Feb 16 2025 08:33:03
%S A124147 2,3,5,7,13,23,113,1327,31397,370261,2010733,20831323,25056082087
%N A124147 Primes p smaller than sqrt(g)*exp(sqrt(g)), where g is the gap between p and the next prime.
%C A124147 Except for 5 & 13, all of the terms here are in A002386 "Increasing gaps between primes ..." at positions 1, 2, 3, 4, 6, 10, 14, 17, 21, 24 & 39. - _Robert G. Wilson v_, Dec 30 2006
%H A124147 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeGaps.html">Prime Gaps</a>
%e A124147 a(9)=31397 because g=72 and sqrt(g)*exp(sqrt(g))=41093.88... > 31397.
%t A124147 NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k] lst = {}; p = 2; Do[q = NextPrim@p; g = q - p; If[p < Sqrt[g]*Exp[Sqrt[g]], Print@p; AppendTo[lst, p]]; p = q, {n, 1235000000}] (* _Robert G. Wilson v_, Dec 30 2006 *)
%Y A124147 Cf. A000040, A001223, A000230.
%K A124147 nonn,more
%O A124147 1,1
%A A124147 _Rémi Eismann_, Dec 13 2006
%E A124147 a(13) from _Robert G. Wilson v_, Dec 30 2006