A093975 Number of prime pairs below 10^n having a difference of 42.
0, 0, 0, 0, 19, 476, 7180, 86637, 954456, 9919519, 99655858, 979052296, 9484975460, 91050561862, 868774394325, 8257228721817, 78288453457352, 741199448968875
Offset: 1
Examples
a(6) = 476 because there are 476 prime gaps of 42 below 10^6.
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]]]],42],{n,10}] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Jun 11 2025 *)
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