Primality proof for n = 152077:
Take b = 2.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 135191, which is a unit, inverse 126977.
23 is prime.
b^((n-1)/23)-1 mod n = 130366, which is a unit, inverse 13687.
(23 * 29) divides n-1.
(23 * 29)^2 > n.
n is prime by Pocklington's theorem.