A055026 Number of Gaussian primes of successive norms (indexed by A055025).

4, 8, 4, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8

Offset: 1

Author

N. J. A. Sloane, Jun 09 2000

Keywords

• nonn
• easy
• nice

Comments

These are the primes in the ring of integers a+bi, a and b rational integers, i = sqrt(-1).

Examples

			There are 8 Gaussian primes of norm 5, +-1+-2i and +-2+-i, but only two inequivalent ones (2+-i).
		

References

• R. K. Guy, Unsolved Problems in Number Theory, A16.
• L. W. Reid, The Elements of the Theory of Algebraic Numbers, MacMillan, NY, 1910, see Chap. V.

Links

• Index entries for Gaussian integers and primes

Crossrefs

Cf. A055025-A055029, A055664-...

Programs

Mathematica

m = 32; Length /@ Split[Sort[Select[Flatten[Table[{a^2 + b^2, a + b*I}, {a, -m, m}, {b, -m, m}], 1], PrimeQ[#[[2]], GaussianIntegers -> True] & ]], #1[[1]] == #2[[1]] & ][[1 ;; 87]] (* Jean-François Alcover, Apr 08 2011 *)

Extensions

More terms from Reiner Martin, Jul 20 2001