Primality proof for n = 139537:
Take b = 2.
b^(n-1) mod n = 1.
19 is prime.
b^((n-1)/19)-1 mod n = 100235, which is a unit, inverse 45420.
17 is prime.
b^((n-1)/17)-1 mod n = 139111, which is a unit, inverse 130038.
3 is prime.
b^((n-1)/3)-1 mod n = 87669, which is a unit, inverse 110313.
(3^3 * 17 * 19) divides n-1.
(3^3 * 17 * 19)^2 > n.
n is prime by Pocklington's theorem.