Primes p for which the polynomial (x^97 - 1)/(x - 1) mod p is irreducible.
5, 7, 13, 17, 23, 29, 37, 41, 59, 71, 83, 97, 107, 137, 157, 173, 179, 181, 199, 211, 223, 233, 251, 277, 281, 317, 331, 347, 349, 359, 367, 373, 383, 401, 409, 499, 523, 541, 569, 577, 587, 599, 619, 641, 653, 719, 739, 761, 769, 797, 859, 863, 883, 887
1
This is the 96th-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 97 == {0, 5, 7, 10, 13, 14, 15, 17, 21, 23, 26, 29, 37, 38, 39, 40, 41, 56, 57, 58, 59, 60, 68, 71, 74, 76, 80, 82, 83, 84, 87, 90, 92}. The fraction of all primes in this sequence is 1/3. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 3.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Cyclotomic polynomial
(Mma) t = {}; n = 97; 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-S000781.
nonn
T. D. Noe, Dec 01 2015