A253939 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6 and (p^6 + 5)/6 are prime.

7309, 45361, 67103, 97777, 128521, 149381, 374669, 543313, 656459, 872747, 940913, 1110817, 1219877, 1288603, 1324567, 1599319, 1629809, 2006677, 2129527, 2495501, 2544121, 2735839, 2763053, 2786363, 2856167, 3145661, 3428839, 3585149, 4063877, 4115971

Offset: 1

Author

Zak Seidov, Jan 20 2015

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..125

Crossrefs

Subsequence of A253925. Cf. A118915, A247478.

Programs

Magma

[p: p in PrimesUpTo(10^7) | IsPrime((p^2+5) div 6) and IsPrime((p^4+5) div 6) and IsPrime((p^6+5) div 6)]; // Vincenzo Librandi, Jan 21 2015

Mathematica

Select[Prime[Range[10^7]], PrimeQ[(#^2 + 5) / 6] &&PrimeQ[(#^4 + 5) / 6] &&PrimeQ[(#^6 + 5) / 6] &] (* Vincenzo Librandi, Jan 21 2015 *)
Select[Prime[Range[3*10^5]],AllTrue[(#^{2,4,6}+5)/6,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 10 2016 *)