A173627 Primes p such that p^2 + 6, p^2 + 12 and p^2 + 18 are all prime.

5, 19, 61, 971, 1451, 2711, 3061, 3449, 6011, 15139, 15241, 21821, 27851, 39839, 51749, 62459, 75679, 76081, 82591, 97001, 121039, 121441, 122299, 135581, 161569, 162671, 196681, 196831, 200881, 214741, 217271, 222931, 242069, 243119, 254161

Offset: 1

Author

Zak Seidov, Nov 09 2010

Keywords

• nonn

Comments

For p > 2, p^2 + 24 is composite (divisible by 5). - Zak Seidov, Sep 07 2018

Links

• Zak Seidov, Table of n, a(n) for n = 1..1800

Crossrefs

Cf. A062718 (p and p^2 + 6 are both prime).

Programs

Magma

[p: p in PrimesUpTo(600000)|IsPrime(p^2+6) and IsPrime(p^2+12) and IsPrime(p^2+18)] // Vincenzo Librandi, Dec 13 2010

Mathematica

okQ[n_]:=Module[{p2=n^2},And@@PrimeQ[{p2+6,p2+12,p2+18}]]; Select[Prime[Range[30000]],okQ] (* Harvey P. Dale, Dec 18 2010 *)

PARI

isok(p) = isprime(p) && isprime(p^2+6) && isprime(p^2+12) && isprime(p^2+18); \\ Michel Marcus, Sep 08 2018