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

1,1

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A355492 A212339 A072111 * A295288 A141397 A305779

Adjacent sequences: A173624 A173625 A173626 * A173628 A173629 A173630

Keyword

nonn

Author

Zak Seidov, Nov 09 2010

Status

approved