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.