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

Author

Enoch Haga, Apr 24 2004

Keywords

• nonn
• more

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

Examples

			a(6) = 140 because there are 140 prime gaps of 54 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.

Crossrefs

Cf. A007508, A093980, A093982.

Programs

Mathematica

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

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