A079796 Primes p such that (3*p)^2 + p^2 + 3^2 and (3*p)^2 - p^2 - 3^2 are both prime.

7, 29, 83, 181, 197, 337, 601, 631, 1303, 1847, 2029, 3023, 3109, 3359, 4591, 4649, 4831, 6397, 6791, 7489, 7559, 7573, 7951, 8609, 8933, 9857, 10151, 10457, 10501, 10709, 11467, 11633, 12011, 12377, 12641, 12739, 13469, 14197, 14449, 14519

Offset

1,1

Comments

Also called nonomatic primes. There is probably an infinity of them. There seems to be no prime number with a similar property using 5 or a larger factor in the polynomials.

Links

Vincenzo Librandi and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Librandi)

Example

a(2) = 29 since (3*29)^2 + 29^2 + 3^2 = 8419 and (3*29)^2 - 29^2 - 3^2 = 6719 are both primes.

Mathematica

Select[Prime@Range[1, 2000], PrimeQ[9 #^2 + #^2 + 9] && PrimeQ[9 #^2 - #^2 - 9] &] (* Vincenzo Librandi, Oct 18 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(15000)| IsPrime( (3*p)^2 + p^2 + 3^2) and IsPrime((3*p)^2 - p^2 - 3^2)]; // Vincenzo Librandi, Oct 18 2012
(PARI) is(n)=isprime(10*n^2+9) && isprime(8*n^2-9) && isprime(n) \\ Charles R Greathouse IV, Jun 10 2015

Crossrefs

Sequence in context: A231988 A141854 A267290 * A242727 A229795 A114043

Adjacent sequences: A079793 A079794 A079795 * A079797 A079798 A079799

Keyword

easy,nonn

Author

Olivier Gérard, Feb 19 2003

Status

approved