A124147 Primes p smaller than sqrt(g)*exp(sqrt(g)), where g is the gap between p and the next prime.

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

Offset: 1

Author

Rémi Eismann, Dec 13 2006

Keywords

• nonn
• more

Comments

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

Examples

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

Links

• Eric Weisstein's World of Mathematics, Prime Gaps

Crossrefs

Cf. A000040, A001223, A000230.

Programs

Mathematica

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 *)

Extensions

a(13) from Robert G. Wilson v, Dec 30 2006