A266970 Primes of the form x^3 + x*y + y^3 where x and y are positive integers.
3, 11, 31, 41, 103, 131, 167, 223, 503, 521, 563, 601, 677, 739, 829, 911, 1361, 1439, 1511, 1613, 1741, 1913, 1931, 2441, 2939, 3191, 3391, 3413, 3499, 3671, 3823, 4007, 4229, 4871, 4931, 4969, 5231, 5851, 6047, 6301, 6329, 7079, 7331, 7523, 7759, 8087, 8263, 8543, 9281, 9283
Offset: 1
Keywords
Examples
11 is a term because 2^3 + 2*1 + 1^3 = 11 is prime. 31 is a term because 3^3 + 3*1 + 1^3 = 31 is prime. 41 is a term because 3^3 + 3*2 + 2^3 = 41 is prime.
Programs
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Mathematica
nn = 10000; lim = Floor[nn^(1/3)]; Union[Reap[Do[p = a^3 + a*b + b^3; If[p <= nn && PrimeQ[p], Sow[p]], {a, lim}, {b, a}]][[2, 1]]] (* Wesley Ivan Hurt, Jan 07 2016 after T. D. Noe *) lim=100; Select[Union[Flatten[Table[x^3 + x y + y^3, {x, 0, lim}, {y, 0, lim}]]], #>0 && #