OFFSET
1,1
COMMENTS
Under Schinzel's hypothesis, there are infinitely many primes of this form.
p must be of form 6k+1 to give an integer. A053182 lists when p^2 + p + 1 is prime. - Jens Kruse Andersen, Aug 06 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..4900
Eric Weisstein's World of Mathematics, Schinzel's Hypothesis.
MAPLE
select(n -> isprime(n) and isprime((n^2 + n + 1)/3), [seq(6*k+1, k=1..1000)]); # Robert Israel, Aug 05 2014
MATHEMATICA
Select[Prime[Range[500]], PrimeQ[(#^2 + # + 1)/3] &]
PROG
(Magma) [p: p in PrimesInInterval(3, 3500)| IsPrime((p^2+p+1) div 3)];
(PARI) forprime(p=1, 10^4, s=(p^2+p+1)/3; if(floor(s)==s, if(isprime(s), print1(p, ", ")))) \\ Derek Orr, Aug 05 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Aug 05 2014
STATUS
approved