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

1,5

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(6) = 476 because there are 476 prime gaps of 42 below 10^6.

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 *)

Crossrefs

Cf. A007508, A093974, A093976.

Sequence in context: A284163 A218477 A003700 * A159248 A348321 A284220

Adjacent sequences: A093972 A093973 A093974 * A093976 A093977 A093978

Keyword

nonn,more,changed

Author

Enoch Haga, Apr 24 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