Primality proof for n = 166571:
Take b = 2.
b^(n-1) mod n = 1.
16657 is prime. b^((n-1)/16657)-1 mod n = 1023, which is a unit, inverse 85158.
(16657) divides n-1.
(16657)^2 > n.
n is prime by Pocklington's theorem.