Primality proof for n = 151883:
Take b = 2.
b^(n-1) mod n = 1.
75941 is prime. b^((n-1)/75941)-1 mod n = 3, which is a unit, inverse 50628.
(75941) divides n-1.
(75941)^2 > n.
n is prime by Pocklington's theorem.