Primes p for which the polynomial (x^67 - 1)/(x - 1) mod p is irreducible.
2, 7, 11, 13, 31, 41, 61, 67, 79, 101, 113, 191, 197, 229, 233, 251, 281, 331, 337, 347, 353, 367, 379, 383, 409, 433, 443, 463, 487, 503, 547, 577, 587, 593, 599, 631, 647, 653, 677, 683, 701, 727, 733, 739, 757, 769, 787, 811, 883, 919, 1033, 1039, 1049, 1051
1
This is the 66th-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 67 == {0, 2, 7, 11, 12, 13, 18, 20, 28, 31, 32, 34, 41, 44, 46, 48, 50, 51, 57, 61, 63}. The fraction of all primes in this sequence is 10/33. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 33/10.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Cyclotomic polynomial
(Mma) t = {}; n = 67; 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