Primality proof for n = 354073:
Take b = 2.
b^(n-1) mod n = 1.
14753 is prime. b^((n-1)/14753)-1 mod n = 135784, which is a unit, inverse 183094.
(14753) divides n-1.
(14753)^2 > n.
n is prime by Pocklington's theorem.