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A243595
Primes p such that 3 + 2*p^2 is also prime.
3
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
1,1
COMMENTS
Corresponding primes 3 + 2*p^2 are congruent to 5 modulo 6.
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Prime[Range[500]], PrimeQ[3 + 2 #^2] &] (* Bruno Berselli, Jun 07 2014 *)
PROG
(PARI) s=[]; forprime(p=2, 4000, if(isprime(3+2*p^2), s=concat(s, p))); s \\ Colin Barker, Jun 07 2014
(Magma) [p: p in PrimesUpTo(4000) | IsPrime(3+2*p^2)]; // Bruno Berselli, Jun 07 2014
(Sage) [p for p in primes(4000) if is_prime(3+2*p^2)] # Bruno Berselli, Jun 07 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Jun 07 2014
STATUS
approved