A093737 Number of prime pairs below 10^n having a difference of 4.
0, 7, 40, 202, 1215, 8143, 58621, 440257, 3424679, 27409998, 224373160, 1870585458, 15834656002, 135779962759, 1177207270203, 10304191320776, 90948823579814, 808675898548205
Offset: 1
Examples
a(2) = 7 because there are 7 prime gaps of 4 below 10^2.
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.
Programs
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PARI
a(n)=my(p=2,s); forprime(q=3,10^n, if(q-p==4, s++); p=q); s \\ Charles R Greathouse IV, Feb 05 2016
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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)
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