A173628 Primes p such that p^3 + 6, p^3 + 12 and p^3 + 18 are all prime.

2351, 6991, 49451, 193751, 223781, 769781, 771431, 779341, 880211, 903871, 1064411, 1066231, 1383191, 1447151, 1745621, 1898371, 1974551, 1999511, 2015411, 2025421, 2435831, 2476421, 2695831, 2805911, 3531041, 3679121

Offset

1,1

Comments

All terms == 1 (mod 10). - Robert Israel, Mar 18 2020

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Maple

filter:= t -> andmap(isprime, [t, t^3+6, t^3+12, t^3+18]):
select(filter, [seq(i, i=1..10^7, 10); # Robert Israel, Mar 18 2020

Mathematica

Select[Prime[Range[300000]], AllTrue[#^3+{6, 12, 18}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 28 2019 *)

Prog

(Magma) [p: p in PrimesUpTo(1000000)|IsPrime(p^3+6) and IsPrime(p^3+12) and IsPrime(p^3+18)] // Vincenzo Librandi, Dec 13 2010

Crossrefs

Cf. A173627 (p, p^2+6, p^2+12 and p^2+18 are all prime).

Sequence in context: A198047 A179137 A003552 * A130023 A219192 A234078

Adjacent sequences: A173625 A173626 A173627 * A173629 A173630 A173631

Keyword

nonn

Author

Zak Seidov, Nov 09 2010

Status

approved