Primality proof for n = 145709:

Take b = 2.

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

499 is prime.
b^((n-1)/499)-1 mod n = 8478, which is a unit, inverse 83854.

(499) divides n-1.

(499)^2 > n.

n is prime by Pocklington's theorem.