A093745 Number of prime pairs below 10^n having a difference of 20.
0, 0, 1, 15, 238, 2401, 22084, 202922, 1824043, 16296072, 145357801, 1298682892, 11638466683, 104682551230, 945244226939, 8568535834789, 77968773245740, 712064159940996
Offset: 1
Examples
a(4) = 15 because there are 15 prime gaps of 20 below 10^4.
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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Mathematica
Table[Length[Select[Partition[Prime[Range[PrimePi[10^i]]], 2, 1], #[[2]] - #[[1]] == 20 &]], {i, 9}] (* Harvey P. Dale, Jan 29 2011 *) -
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