A201719 Primes of the form x^2 + 2y^2 such that y^2 + 2x^2 is also prime.

11, 19, 43, 59, 67, 83, 107, 139, 163, 179, 211, 251, 307, 331, 419, 443, 467, 491, 563, 571, 587, 619, 643, 811, 883, 907, 947, 971, 1019, 1091, 1123, 1171, 1259, 1291, 1307, 1427, 1531, 1571, 1579, 1667, 1699, 1747, 1787, 1811, 1907, 1979, 1987, 2003, 2011

Offset: 1

Author

Zak Seidov, Dec 04 2011

Keywords

• nonn

Comments

All terms == 3 mod 8 (cf. A007520).

Examples

			Corresponding pairs of primes:
(a(1),a(2))=(11,19): 11=3^2+2*1^2, 19=1^2+2*3^2
(a(3),a(4))=(43,59): 43=5^2+2*3^2, 59=3^2+2*5^2
(a(5),a(7))=(67,107): 67=7^2+2*3^2, 107=3^2+2*7^2.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A154777.

Programs

Mathematica

With[{nn=50},Take[Union[Flatten[Select[{#[[1]]^2+2#[[2]]^2,2#[[1]]^2+ #[[2]]^2}&/@Subsets[Range[nn],{2}],And@@PrimeQ[#]&]]],nn]] (* Harvey P. Dale, Sep 15 2013 *)