A253940 Primes p such that (p^2 + 5)/6, (p^4 + 5)/6, and (p^8 + 5)/6 are prime.

39367, 52163, 67103, 79631, 100981, 280547, 318457, 530711, 605123, 815401, 833923, 834947, 928871, 1313857, 1734067, 1750069, 1800973, 2163979, 2427137, 2598119, 2611027, 2754991, 2764187, 2836259, 3040757, 3101309, 3118697, 3465953, 3646693, 4014809

Offset

1,1

Links

R. J. Mathar, Table of n, a(n) for n = 1..108

Mathematica

Select[Prime[Range[10^6]], PrimeQ[(#^2 + 5) / 6] &&PrimeQ[(#^4 + 5) / 6] &&PrimeQ[(#^8 + 5) / 6] &] (* Vincenzo Librandi, Jan 21 2015 *)
Select[Prime[Range[300000]], AllTrue[({#^2, #^4, #^8}+5)/6, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 15 2021 *)

Prog

(Magma) [p: p in PrimesUpTo(10^7) | IsPrime((p^2+5) div 6) and IsPrime((p^4+5) div 6) and IsPrime((p^8+5) div 6)]; // Vincenzo Librandi, Jan 21 2015

Crossrefs

Subsequence of A253925. Cf. A118915, A247478, A253939.

Sequence in context: A274128 A144306 A234033 * A183833 A203875 A252604

Adjacent sequences: A253937 A253938 A253939 * A253941 A253942 A253943

Keyword

nonn

Author

Zak Seidov, Jan 20 2015

Status

approved