Number of pairs of numbers (n,x) with 0 < x <= n such that n^16 + x^16 is prime.
1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 1, 2, 2, 1, 0, 2, 3, 3, 2, 0, 0, 2, 3, 2, 0, 1, 2, 1, 3, 3, 1, 4, 2, 2, 6, 5, 2, 4, 1, 0, 3, 0, 0, 5, 1, 0, 2, 2, 2, 5, 4, 1, 4, 3, 0, 7, 0, 5, 2, 5, 0, 5, 4, 2, 3, 4, 6, 4, 3, 1, 5, 6, 2, 5, 4, 4, 7, 6, 1, 4, 2, 2
1
It appears that for n > 135, there is an x in the range [0,n] such that n^16 + x^16 is prime.
T. D. Noe, Plot of 5000 terms
T. D. Noe, Table of 5000 terms
(Mma) Table[cnt = 0; Do[If[PrimeQ[x^16 + y^16], cnt++], {y, x}]; cnt, {x, 100}]
nonn
T. D. Noe, Apr 24 2015