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A370830 Primes p such that the polynomial x^4-x^3-x^2-x-1 is irreducible mod p.

%I A370830 #29 Mar 22 2024 17:21:33
%S A370830 2,5,31,43,53,79,83,89,97,109,131,139,151,199,229,233,239,283,313,317,
%T A370830 359,367,389,433,443,479,487,569,571,577,601,617,641,643,659,677,769,
%U A370830 797,823,853,857,929,937,941,971,1013,1019,1049,1063,1069,1087,1093,1117,1163,1171,1181,1231,1249,1283
%N A370830 Primes p such that the polynomial x^4-x^3-x^2-x-1 is irreducible mod p.
%H A370830 Robert Israel, <a href="/A370830/b370830.txt">Table of n, a(n) for n = 1..10000</a>
%p A370830 P:= x^4 - x^3 - x^2 - x - 1:
%p A370830 select(p -> Irreduc(P) mod p, [seq(ithprime(i),i=1..1000)]);
%o A370830 (Python)
%o A370830 from itertools import islice
%o A370830 from sympy import Poly, nextprime
%o A370830 from sympy.abc import x
%o A370830 def A370830_gen(): # generator of terms
%o A370830     p = 2
%o A370830     while True:
%o A370830         if Poly(x*(x*(x*(x-1)-1)-1)-1, x, modulus=p).is_irreducible:
%o A370830             yield p
%o A370830         p = nextprime(p)
%o A370830 A370830_list = list(islice(A370830_gen(),20)) # _Chai Wah Wu_, Mar 14 2024
%Y A370830 Subsequence of A106283. Cf. 106309.
%K A370830 nonn
%O A370830 1,1
%A A370830 _Robert Israel_, Mar 13 2024