Number of pairs of numbers (n,x) with 0 < x <= n such that n^4 + x^4 is prime.

1, 1, 1, 2, 2, 1, 3, 2, 2, 2, 3, 0, 3, 2, 2, 4, 4, 3, 6, 4, 2, 2, 5, 5, 3, 7, 3, 5, 5, 5, 2, 6, 3, 10, 3, 5, 8, 5, 6, 4, 9, 6, 9, 3, 6, 9, 8, 4, 6, 8, 7, 6, 13, 8, 6, 7, 5, 7, 9, 4, 8, 14, 3, 7, 7, 6, 7, 10, 9, 4, 14, 5, 10, 13, 5, 10, 9, 6, 14, 6, 8, 12, 11, 7

1

It appears that for every n except 12, there is an x in the range [0,n] such that n^4 + x^4 is prime.

T. D. Noe, Plot of 5000 terms

T. D. Noe, Table of 5000 terms

(Mma) Table[cnt = 0; Do[If[PrimeQ[x^4 + y^4], cnt++], {y, x}]; cnt, {x, 100}]

nonn

T. D. Noe, Apr 24 2015