A093752 Number of prime pairs below 10^n having a difference of 34.

0, 0, 0, 2, 33, 557, 6721, 71248, 719531, 6996756, 66745265, 629634308, 5900013825, 55082083947, 513336390285, 4781421106831, 44546412612392, 415327075240821

Offset

1,4

Links

Table of n, a(n) for n=1..18.

Siegfried "Zig" Herzog, Frequency of Occurrence of Prime Gaps

T. Oliveira e Silva, S. Herzog, and S. Pardi, Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4.10^18, Math. Comp., 83 (2014), 2033-2060.

Example

a(5) = 33 because there are 33 prime gaps of 34 below 10^n.

Mathematica

Table[Count[Differences[Prime[Range[PrimePi[10^n]]]], 34], {n, 13}] (* The program takes a long time to run *) (* Harvey P. Dale, Nov 24 2017 *)

Crossrefs

Cf. A007508, A093751, A093972.

Sequence in context: A231794 A083143 A064008 * A045984 A077657 A219342

Adjacent sequences: A093749 A093750 A093751 * A093753 A093754 A093755

Keyword

nonn,more

Author

Enoch Haga, Apr 15 2004

Extensions

a(10)-a(13) from Washington Bomfim, Jun 22 2012

a(14)-a(18) from S. Herzog's website added by Giovanni Resta, Aug 14 2018

Status

approved