Select[Range[3000], AllTrue[#^4+#+{1, -1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 13 2017 *)
PROG
(Python)
import sympy
from sympy import isprime
{print(n) for n in range(10**4) if isprime(n**4+n-1) and isprime(n**4+n+1)}
(PARI)
s=[]; for(n=1, 3000, if(isprime(n^4+n+1)&&isprime(n^4+n-+1), s=concat(s, n))); s \\ Colin Barker, Jan 31 2014
(Magma) [n: n in [1..5*10^3] |IsPrime(n^4+n-1) and IsPrime(n^4 +n+1)]; // Vincenzo Librandi, Dec 26 2015
