A093740 Number of prime pairs below 10^n having a difference of 10.

0, 0, 16, 119, 916, 7079, 54431, 430016, 3484767, 28764495, 241298621, 2052293026, 17663498098, 153590992984, 1347587381486, 11917605558274, 106139298948562, 951243890034661

Offset

1,3

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(3) = 16 because there are 16 prime gaps of 10 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, A093739, A093741.

Sequence in context: A250169 A210428 A283037 * A303724 A305227 A304772

Adjacent sequences: A093737 A093738 A093739 * A093741 A093742 A093743

Keyword

nonn,more

Author

Enoch Haga, Apr 15 2004

Extensions

a(10)-a(13) from Washington Bomfim, Jun 20 2012

a(14)-a(18) from S. Herzog's website added by Giovanni Resta, Aug 14 2018

Status

approved