A093979 Number of prime pairs below 10^n having a difference of 50.

0, 0, 0, 0, 5, 106, 2048, 27522, 328066, 3607750, 37931633, 386726111, 3862450797, 38030383640, 370777525300, 3589909796035, 34588559153345, 332118860517515

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(5) = 5 because there are 5 prime gaps of 50 below 10^5.

Mathematica

a[n_] := Length@Select[Select[Range[1, 10^n - 50], PrimeQ[#] &], 50 == NextPrime[#] - # &]
a /@ Range[1, 6] (* Julien Kluge, Dec 03 2016 *)
Table[Count[Differences[Prime[Range[PrimePi[10^n]]]], 50], {n, 10}] (* To get additional terms, increase the "n, 10" variable specification to "n, x" where x is greater than 10 but not greater than 14 (because "n, 10^14" is the highest value Mathematica version 11 can compute) but the program will take a long time to run *) (* Harvey P. Dale, Aug 12 2018 *)

Crossrefs

Cf. A007508, A093978, A093980.

Sequence in context: A015002 A059490 A204109 * A293261 A324230 A142479

Adjacent sequences: A093976 A093977 A093978 * A093980 A093981 A093982

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