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A243595 Primes p such that 3 + 2*p^2 is also prime.

%I A243595 #20 Sep 08 2022 08:46:08
%S A243595 2,5,7,23,37,43,47,83,103,107,113,127,197,373,433,463,467,523,547,587,
%T A243595 593,617,733,743,797,863,877,887,953,1097,1163,1213,1297,1427,1493,
%U A243595 1567,1583,1657,1667,1693,1783,1877,1987,2053,2063,2087,2207,2357,2557,2753
%N A243595 Primes p such that 3 + 2*p^2 is also prime.
%C A243595 Corresponding primes 3 + 2*p^2 are congruent to 5 modulo 6.
%H A243595 Bruno Berselli, <a href="/A243595/b243595.txt">Table of n, a(n) for n = 1..1000</a>
%e A243595 2 is in the sequence because 3+2*2^2 = 11 is prime; also, for the comment, 11 = 6+5.
%e A243595 5 is in the sequence because 3+2*5^2 = 53 is prime, also 53 = 6*8+5.
%e A243595 7 is in the sequence because 3+2*7^2 = 101 is prime, also 101 = 6*16+5.
%t A243595 Select[Prime[Range[500]], PrimeQ[3 + 2 #^2] &] (* _Bruno Berselli_, Jun 07 2014 *)
%o A243595 (PARI) s=[]; forprime(p=2, 4000, if(isprime(3+2*p^2), s=concat(s, p))); s \\ _Colin Barker_, Jun 07 2014
%o A243595 (Magma) [p: p in PrimesUpTo(4000) | IsPrime(3+2*p^2)]; // _Bruno Berselli_, Jun 07 2014
%o A243595 (Sage) [p for p in primes(4000) if is_prime(3+2*p^2)] # _Bruno Berselli_, Jun 07 2014
%Y A243595 Cf. A002476, A033203, A153507, A161724.
%K A243595 nonn,easy
%O A243595 1,1
%A A243595 _Zak Seidov_, Jun 07 2014