Primes p for which the polynomial (x^89 - 1)/(x - 1) mod p is irreducible.
3, 7, 13, 19, 23, 29, 31, 41, 43, 59, 61, 83, 89, 103, 113, 127, 137, 149, 151, 163, 181, 191, 193, 197, 211, 229, 239, 241, 281, 293, 313, 337, 349, 353, 359, 379, 383, 389, 397, 419, 421, 431, 439, 491, 499, 503, 521, 541, 547, 557, 563, 569, 577, 593
1
This is the 88th-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 89 == {0, 3, 6, 7, 13, 14, 15, 19, 23, 24, 26, 27, 28, 29, 30, 31, 33, 35, 38, 41, 43, 46, 48, 51, 54, 56, 58, 59, 60, 61, 62, 63, 65, 66, 70, 74, 75, 76, 82, 83, 86}. The fraction of all primes in this sequence is 5/11. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 11/5.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Cyclotomic polynomial
(Mma) t = {}; n = 89; p = 1; While[Length[t] < 100, p = NextPrime[p]; If[Length[FactorList[(x^n - 1)/(x - 1), Modulus -> p]] == 2, AppendTo[t, p]]]; t
Cf. A045309, A042993, A045401, S000762-S000782.
nonn
T. D. Noe, Dec 01 2015