Primality proof for n = 166823:
Take b = 2.
b^(n-1) mod n = 1.
349 is prime.
b^((n-1)/349)-1 mod n = 122817, which is a unit, inverse 148964.
239 is prime.
b^((n-1)/239)-1 mod n = 85940, which is a unit, inverse 120804.
(239 * 349) divides n-1.
(239 * 349)^2 > n.
n is prime by Pocklington's theorem.