

A093979


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


2



0, 0, 0, 0, 5, 106, 2048, 27522, 328066, 3607750, 37931633, 386726111, 3862450797, 38030383640, 370777525300, 3589909796035, 34588559153345, 332118860517515
(list;
graph;
refs;
listen;
history;
text;
internal format)



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), 20332060.


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 A142479 A204110
Adjacent sequences: A093976 A093977 A093978 * A093980 A093981 A093982


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



