Primality proof for n = 32573:

Take b = 2.

b^(n-1) mod n = 1.

479 is prime.
b^((n-1)/479)-1 mod n = 10720, which is a unit, inverse 30759.

(479) divides n-1.

(479)^2 > n.

n is prime by Pocklington's theorem.