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%I #19 Sep 08 2022 08:45:50
%S 2351,6991,49451,193751,223781,769781,771431,779341,880211,903871,
%T 1064411,1066231,1383191,1447151,1745621,1898371,1974551,1999511,
%U 2015411,2025421,2435831,2476421,2695831,2805911,3531041,3679121
%N Primes p such that p^3 + 6, p^3 + 12 and p^3 + 18 are all prime.
%C All terms == 1 (mod 10). - _Robert Israel_, Mar 18 2020
%H Robert Israel, <a href="/A173628/b173628.txt">Table of n, a(n) for n = 1..1000</a>
%p filter:= t -> andmap(isprime, [t,t^3+6,t^3+12, t^3+18]):
%p select(filter, [seq(i,i=1..10^7,10); # _Robert Israel_, Mar 18 2020
%t 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 *)
%o (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
%Y Cf. A173627 (p, p^2+6, p^2+12 and p^2+18 are all prime).
%K nonn
%O 1,1
%A _Zak Seidov_, Nov 09 2010
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