Primality proof for n = 158769362377:

Take b = 2.

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

59598109 is prime.
b^((n-1)/59598109)-1 mod n = 1812215223, which is a unit, inverse 61280220467.

(59598109) divides n-1.

(59598109)^2 > n.

n is prime by Pocklington's theorem.