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
Examples
a(5) = 33 because there are 33 prime gaps of 34 below 10^n.
Links
- 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.
Programs
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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 *)
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