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.