Pairs of positive numbers x <= y such that x^64 + y^64 is prime.

1, 1, 8, 11, 6, 13, 7, 16, 14, 17, 12, 29, 3, 32, 27, 32, 2, 37, 7, 38, 23, 38, 4, 39, 10, 41, 6, 49, 14, 51, 3, 52, 2, 53, 4, 55, 36, 55, 21, 58, 47, 60, 36, 61, 51, 62, 10, 63, 20, 63, 15, 64, 43, 64, 51, 64, 19, 66, 30, 67, 26, 69, 52, 69, 17, 70, 37, 70

1

Except for the first pair, numbers in a pair have opposite parity. See S000596 for the pairs sorted by the primes they generate.

T. D. Noe, Plot of 2503 pairs

T. D. Noe, Table of 2503 pairs

(Mma) t = {}; x = 0; While[Length[t] < 50, x++; Do[If[PrimeQ[x^64 + y^64], AppendTo[t, {y, x}]], {y, x}]]

Cf. S000585-S000589, S000596, S000602.

nonn

T. D. Noe, Apr 22 2015