Gaussian primes in the first quadrant, sorted by magnitude and real part.
1, 1, 1, 2, 2, 1, 3, 0, 2, 3, 3, 2, 1, 4, 4, 1, 2, 5, 5, 2, 1, 6, 6, 1, 4, 5, 5, 4, 7, 0, 2, 7, 7, 2, 5, 6, 6, 5, 3, 8, 8, 3, 5, 8, 8, 5, 4, 9, 9, 4, 1, 10, 10, 1, 3, 10, 10, 3, 7, 8, 8, 7, 11, 0, 4, 11, 11, 4, 7, 10, 10, 7, 6, 11, 11, 6, 2, 13, 13, 2, 9, 10, 10
1
Note that after the first Gaussian prime 1+i, all primes are either real (such as 3+0i) or come in pairs (such as 1+2i and 2+i).
T. D. Noe, Plot of 1232 pairs
T. D. Noe, Table of 1232 pairs
T. D. Noe, Numbers plotted in the complex plane
Eric W. Weisstein, MathWorld: Gaussian Prime
(Mma) nn = 10; t = Select[Flatten[Table[a + b*I, {a, nn}, {b, 0, nn}]], Abs[#] <= nn && PrimeQ[#, GaussianIntegers -> True] &]; t2 = Sort[t, Abs[#1] <= Abs[#2] &]; Flatten[Transpose[{Re /@ t2, Im /@ t2}]]
nonn
T. D. Noe, Dec 14 2014