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

2, 5, 7, 23, 37, 43, 47, 83, 103, 107, 113, 127, 197, 373, 433, 463, 467, 523, 547, 587, 593, 617, 733, 743, 797, 863, 877, 887, 953, 1097, 1163, 1213, 1297, 1427, 1493, 1567, 1583, 1657, 1667, 1693, 1783, 1877, 1987, 2053, 2063, 2087, 2207, 2357, 2557, 2753

Offset: 1

Author

Zak Seidov, Jun 07 2014

Keywords

• nonn
• easy

Comments

Corresponding primes 3 + 2*p^2 are congruent to 5 modulo 6.

Examples

			2 is in the sequence because 3+2*2^2 = 11 is prime; also, for the comment, 11 = 6+5.
5 is in the sequence because 3+2*5^2 = 53 is prime, also 53 = 6*8+5.
7 is in the sequence because 3+2*7^2 = 101 is prime, also 101 = 6*16+5.
		

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002476, A033203, A153507, A161724.

Programs

Magma

[p: p in PrimesUpTo(4000) | IsPrime(3+2*p^2)]; // Bruno Berselli, Jun 07 2014

Mathematica

Select[Prime[Range[500]], PrimeQ[3 + 2 #^2] &] (* Bruno Berselli, Jun 07 2014 *)

PARI

s=[]; forprime(p=2, 4000, if(isprime(3+2*p^2), s=concat(s, p))); s \\ Colin Barker, Jun 07 2014

Sage

[p for p in primes(4000) if is_prime(3+2*p^2)] # Bruno Berselli, Jun 07 2014