Primes p for which the polynomial (x^61 - 1)/(x - 1) mod p is irreducible.
2, 7, 17, 31, 43, 59, 61, 67, 71, 79, 139, 157, 173, 181, 193, 227, 251, 307, 311, 331, 349, 359, 373, 383, 397, 401, 409, 421, 433, 457, 523, 547, 593, 617, 641, 653, 661, 673, 677, 701, 739, 787, 811, 823, 941, 983, 1019, 1031, 1039, 1063, 1091, 1129, 1153
1
This is the 60th-degree cyclotomic polynomial. These primes p satisfy the congruence p mod 61 == {0, 2, 6, 7, 10, 17, 18, 26, 30, 31, 35, 43, 44, 51, 54, 55, 59}. The fraction of all primes in this sequence is 4/15. If we plotted n versus primepi(s(n)), then the plotted points would be very close to the line having slope 15/4.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
Wikipedia, Cyclotomic polynomial
(Mma) t = {}; n = 61; 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