A093982 -id:A093982 - cp's OEIS frontend

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

Enoch Haga, Apr 24 2004

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

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

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.

Cf. A007508, A093980, A093982.

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

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

A093983 Number of prime pairs below 10^n having a difference of 58.

Original entry on oeis.org

0, 0, 0, 0, 4, 54, 1052, 14611, 181948, 2096211, 22788376, 238482555, 2433024862, 24386079471, 241344901528, 2366884988610, 23059199264485, 223571124198381

Offset: 1

Enoch Haga, Apr 24 2004

			a(7) = 1052 because there are 1052 prime gaps of 58 below 10^7.

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.

Cf. A007508, A093982, A093984.

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

cp's OEIS Frontend

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

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