A093744 Number of prime pairs below 10^n having a difference of 18.

0, 0, 1, 40, 514, 4909, 43851, 384738, 3351032, 29189691, 255371697, 2246576317, 19878698732, 176913444597, 1583135619012, 14240370591853, 128711774414592, 1168583066366245

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) = 40 because there are 40 prime gaps of 18 below 10^4.

Mathematica

Table[Count[Differences[Prime[Range[PrimePi[10^n]]]], 18], {n, 8}] (* The program generates the first 8 terms in the sequence. To generate more increase the n constant but the program may take a long time to run. *) (* Harvey P. Dale, Sep 03 2021 *)

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, A093743, A093745.

Sequence in context: A140045 A223162 A069079 * A109105 A269692 A247409

Adjacent sequences: A093741 A093742 A093743 * A093745 A093746 A093747

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