A091101 Number of first-quadrant Gaussian primes whose norm is less than 10^n.

5, 27, 173, 1245, 9635, 78525, 664811, 5762247, 50850399, 455056167

Offset: 1

Author

T. D. Noe, Dec 19 2003

Keywords

• nonn
• more

Links

• 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), A091100, A091102.

Programs

Mathematica

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

Formula

a(2n) = 2*A091098(2n) + 2*A091099(n) + 1.

Extensions

a(10) calculated from the data at A091098 and A091099 by Amiram Eldar, Feb 28 2020