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
Keywords
Links
- R. J. Mathar, Table of n, a(n) for n = 1..108
Programs
-
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
-
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 *)