A091100 Number of Gaussian primes whose norm is less than 10^n.

16, 100, 668, 4928, 38404, 313752, 2658344, 23046512, 203394764, 1820205436, 16472216912, 150431552012, 1384262129028, 12819767598972, 119378281788240, 1116953361826164

Offset: 1

Author

T. D. Noe, Dec 19 2003

Keywords

• nonn

Links

• Marc Deléglise, Pierre Dusart, and Xavier-Francois Roblot, Counting primes in residue classes, Math. Comp. 73 (2004), no. 247, 1565-1575
• Eric Weisstein's World of Mathematics, Gaussian Prime
• Index entries for Gaussian integers and primes

Crossrefs

Cf. A091098 (number of primes of the form 4k+1 less than 10^n), A091099 (number of primes of the form 4k+3 less than 10^n), A091101, A091102.

Cf. A091134 (number of Gaussian primes whose modulus is less than 10^n).

Cf. A017934, A295996.

Programs

Mathematica

Table[lim2=10^n; lim1=Floor[Sqrt[lim2]]; cnt=0; Do[If[x^2+y^2True], cnt++ ], {x, -lim1, lim1}, {y, -lim1, lim1}]; cnt, {n, 6}]

Formula

a(2n) = 8*A091098(2n) + 4*A091099(n) + 4.

a(n) ~ 4 Li(10^n) ~ k/n * 10^n, where k = 4/log(10) = 1.737.... - Charles R Greathouse IV, Oct 24 2012

Extensions

a(10)-a(16) from Seiichi Manyama using the data in A091098, Dec 03 2017