A093741 Number of prime pairs below 10^n having a difference of 12.
0, 0, 7, 105, 964, 8005, 65513, 538382, 4468957, 37588207, 319972455, 2753597777, 23931289984, 209796541197, 1853552707266, 16490531511496, 147632682729513, 1329180643501191
Offset: 1
Examples
a(3) = 7 because there are 7 prime gaps of 12 below 10^3.
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[Count[Differences[Prime[Range[PrimePi[10^n]]]],12],{n,10}] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Jun 24 2025 *) -
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