A093743 Number of prime pairs below 10^n having a difference of 16.

0, 0, 0, 33, 339, 2881, 25099, 215804, 1846097, 15888305, 137715130, 1202533145, 10576414202, 93649741408, 834451865580, 7478286927272, 67376249426987, 609996708149171

Offset

1,4

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(4) = 33 because there are 33 prime gaps of 16 below 10^3.

Prog

(UBASIC) 20 N=1:dim T(34); 30 A=nxtprm(N); 40 N=A; 50 B=nxtprm(N); 60 D=B-A; 70 for x=2 to 34 step 2; 80 if D=X and B<10^2+1 then T(X)=T(X)+1; 90 next X; 100 if B>10^2+1 then 140; 110 B=A; 120 N=N+1; 130 goto 30; 140 for x=2 to 34 step 2; 150 print T(X); , 160 next (This program simultaneously finds values from 2 to 34 - if gap=2 add 1- adjust lines 80 and 100 for desired 10^n)

Crossrefs

Cf. A007508, A093742, A093744.

Sequence in context: A258638 A081932 A121994 * A279638 A209359 A264282

Adjacent sequences: A093740 A093741 A093742 * A093744 A093745 A093746

Keyword

nonn,more

Author

Enoch Haga, Apr 15 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