A093981 Number of prime pairs below 10^n having a difference of 54.

0, 0, 0, 0, 4, 140, 2403, 33593, 410754, 4627165, 49484726, 511589763, 5167085638, 51359117940, 504751212449, 4920758221226, 47694473239363, 460356869024451

Offset

1,5

Comments

The primes must be consecutive, i.e., there must be no other primes between p and (p+54). - Harvey P. Dale, Aug 08 2011

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) = 140 because there are 140 prime gaps of 54 below 10^6.

Mathematica

Table[Count[Partition[Prime[Range[PrimePi[10^i]]], 2, 1], _?(Last[#] - First[#] == 54&)], {i, 9}] (* Harvey P. Dale, Aug 08 2011 *)

Crossrefs

Cf. A007508, A093980, A093982.

Sequence in context: A221675 A340838 A291450 * A055304 A270065 A002917

Adjacent sequences: A093978 A093979 A093980 * A093982 A093983 A093984

Keyword

nonn,more

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