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.