Pairs of positive numbers x <= y such that x^2 + y^2 is prime.

1, 1, 1, 2, 2, 3, 1, 4, 2, 5, 4, 5, 1, 6, 5, 6, 2, 7, 3, 8, 5, 8, 7, 8, 4, 9, 1, 10, 3, 10, 7, 10, 9, 10, 4, 11, 6, 11, 7, 12, 2, 13, 8, 13, 10, 13, 12, 13, 1, 14, 9, 14, 11, 14, 2, 15, 4, 15, 14, 15, 1, 16, 5, 16, 9, 16, 2, 17, 8, 17, 10, 17, 12, 17, 5, 18

1

Except for the first pair, numbers in a pair have opposite parity. See S000591 for the pairs sorted by the primes they generate.

T. D. Noe, Plot of 2508 pairs

T. D. Noe, Table of 2508 pairs

(Mma) t = {}; x = 0; While[Length[t] < 50, x++; Do[If[PrimeQ[x^2 + y^2], AppendTo[t, {y, x}]], {y, x}]]

Cf. S000586-S000590, S000591, S000597.

nonn

T. D. Noe, Apr 22 2015