Primality proof for n = 177481:
Take b = 2.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 170427, which is a unit, inverse 105296.
17 is prime.
b^((n-1)/17)-1 mod n = 61375, which is a unit, inverse 154214.
(17 * 29) divides n-1.
(17 * 29)^2 > n.
n is prime by Pocklington's theorem.