Pairs of positive numbers x <= y such that x^4 + y^4 is prime.

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

1

Except for the first pair, numbers in a pair have opposite parity. See S000592 for the pairs sorted by the primes they generate.

T. D. Noe, Plot of 2507 pairs

T. D. Noe, Table of 2507 pairs

(Mma) t = {}; x = 0; While[Length[t] < 50, x++; Do[If[PrimeQ[x^4 + y^4], AppendTo[t, {y, x}]], {y, x}]]

Cf. S000585-S000590, S000592, S000598.

nonn

T. D. Noe, Apr 22 2015