A379881 Prime numbers of the form 8*x^2 + 27*y^2 where x and y are positive integers.

59, 227, 251, 419, 443, 683, 827, 1187, 1451, 1523, 1811, 2027, 2243, 2339, 2579, 2699, 3299, 3371, 3467, 3539, 3659, 3779, 4211, 4259, 4523, 4547, 4691, 5387, 5531, 5651, 6131, 6203, 6299, 6323, 6947, 6971, 7043, 7187, 7451, 7499, 7643, 8123, 8219, 8363, 8387, 8867, 8963, 9011, 9371, 9491, 9539, 9851, 9923

Offset: 1

Author

Steven Lu, Feb 16 2025

Keywords

• nonn
• easy

Comments

All terms are congruent to 11 modulo 24.

Examples

			59 = 8 * 2^2 + 27 * 1^2
227 = 8 * 5^2 + 27 * 1^2
251 = 8 * 1^2 + 27 * 3^2
		

Crossrefs

Intersection of A107161 and A002145.

Programs

Mathematica

With[{limit = 10000}, Sort[DeleteDuplicates[Select[Flatten[Table[8 x^2 + 27 y^2, {x, Floor[Sqrt[limit/8]]}, {y, Floor[Sqrt[limit/27]]}]], PrimeQ[#] && # < limit &]]]]