A189051 Numbers n such that n+/-2 and n^2+/-2 are all primes.

9, 15, 21, 309, 441, 1611, 2955, 3081, 3879, 5529, 7209, 7755, 7875, 13761, 15015, 15729, 16659, 21561, 22155, 35595, 37059, 38199, 45291, 50049, 51429, 59619, 63855, 67215, 67941, 71331, 72891, 83061, 96459, 96909, 102795, 106959, 111495

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 16 2011

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A087679, A108701.

Programs

Magma

[n: n in [1..2000000]|IsPrime(n-2)and IsPrime(n+2)and IsPrime(n^2-2)and IsPrime(n^2+2)]; // Vincenzo Librandi, Apr 20 2011

Maple

select(n -> isprime(n-2) and isprime(n+2) and isprime(n^2-2) and isprime(n^2+2),
[seq(i,i=3..10^6, 6)]); # Robert Israel, Jun 23 2017

Mathematica

pQ[n_]:=Module[{n2=n^2},And@@PrimeQ[{n+2,n-2,n2+2,n2-2}]]; Select[Range[ 120000],pQ] (* Harvey P. Dale, Jun 04 2011 *)

PARI

forstep(n=3,100000,6,if(isprime(n-2)&isprime(n+2)&isprime(n^2-2)&isprime(n^2+2),print1(n", ")))

Formula

Intersection of A087679 and A108701.

Extensions

Corrected and extended by Franklin T. Adams-Watters, Apr 16 2011