%I #15 Feb 18 2023 20:50:43
%S 11,41,83,107,113,227,347,443,521,563,593,641,827,929,953,1091,1187,
%T 1193,1259,1409,1427,1553,1601,1697,1811,1979,2003,2297,2339,2393,
%U 2699,2801,2819,3011,3089,3209,3251,3449,3467,3929,3947
%N Primes of the form m^2 + 2*k^2 such that m^2 + 2*(k+1)^2 is also prime.
%C Primes of the form m^2 + 2*k^2 are norms of prime elements of Z[i*sqrt(2)]. Prime couples of the form (m^2 + 2*k^2, m^2 + 2*(k+1)^2) correspond to primes in Z[i*sqrt(2)] differing from i*sqrt(2).
%C A prime cannot be simultaneously the lesser of one such couple and the greater of another.
%F If (m^2 + 2*k^2, m^2 + 2*(k+1)^2) is a prime couple, then m is congruent to 3 modulo 6 and k is congruent to 1 modulo 3.
%e The first 3 prime couples of the form (m^2 + 2*k^2, m^2 + 2*(k+1)^2) are (11,17) = (3^2 + 2*1^2, 3^2 + 2*2^2), (41,59) = (3^2 + 2*4^2, 3^2 + 2*5^2) and (83,89) = (9^2 + 2*1^2, 9^2 + 2*2^2).
%Y See A360155 for greater values.
%Y Cf. A000040 (prime numbers).
%Y Cf. A033203 (primes of form m^2 + 2*k^2).
%K nonn
%O 1,1
%A _Ludovic Schwob_, Jan 28 2023
