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

2, 5, 31, 43, 53, 79, 83, 89, 97, 109, 131, 139, 151, 199, 229, 233, 239, 283, 313, 317, 359, 367, 389, 433, 443, 479, 487, 569, 571, 577, 601, 617, 641, 643, 659, 677, 769, 797, 823, 853, 857, 929, 937, 941, 971, 1013, 1019, 1049, 1063, 1069, 1087, 1093, 1117, 1163, 1171, 1181, 1231, 1249, 1283

Offset: 1

Author

Robert Israel, Mar 13 2024

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A106283. Cf. 106309.

Programs

Maple

P:= x^4 - x^3 - x^2 - x - 1:
select(p -> Irreduc(P) mod p, [seq(ithprime(i),i=1..1000)]);

Python

from itertools import islice
from sympy import Poly, nextprime
from sympy.abc import x
def A370830_gen(): # generator of terms
    p = 2
    while True:
        if Poly(x*(x*(x*(x-1)-1)-1)-1, x, modulus=p).is_irreducible:
            yield p
        p = nextprime(p)
A370830_list = list(islice(A370830_gen(),20)) # Chai Wah Wu, Mar 14 2024