Primes p for which the polynomial (x^71 - 1)/(x - 1) mod p is irreducible.
7, 11, 13, 31, 47, 53, 59, 61, 67, 71, 113, 127, 139, 149, 163, 173, 197, 211, 241, 257, 269, 281, 317, 331, 337, 347, 349, 353, 383, 397, 433, 439, 457, 461, 479, 487, 491, 541, 599, 601, 631, 661, 683, 691, 701, 743, 757, 769, 773, 809, 823, 859, 863, 883
1
This is the 70th-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 71 == {0, 7, 11, 13, 21, 22, 28, 31, 33, 35, 42, 44, 47, 52, 53, 55, 56, 59, 61, 62, 63, 65, 67, 68, 69}. The fraction of all primes in this sequence is 12/35. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 35/12.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Cyclotomic polynomial
(Mma) t = {}; n = 71; 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