Primality proof for n = 545358713:

Take b = 2.

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

28181 is prime.
b^((n-1)/28181)-1 mod n = 420071725, which is a unit, inverse 160797069.

(28181) divides n-1.

(28181)^2 > n.

n is prime by Pocklington's theorem.