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Primes p smaller than sqrt(g)*exp(sqrt(g)), where g is the gap between p and the next prime.
1

%I #17 Feb 10 2018 07:30:23

%S 2,3,5,7,13,23,113,1327,31397,370261,2010733,20831323,25056082087

%N Primes p smaller than sqrt(g)*exp(sqrt(g)), where g is the gap between p and the next prime.

%C 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeGaps.html">Prime Gaps</a>

%e a(9)=31397 because g=72 and sqrt(g)*exp(sqrt(g))=41093.88... > 31397.

%t 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 Cf. A000040, A001223, A000230.

%K nonn,more

%O 1,1

%A _RĂ©mi Eismann_, Dec 13 2006

%E a(13) from _Robert G. Wilson v_, Dec 30 2006