Primality proof for n = 235251347:
Take b = 2.
b^(n-1) mod n = 1.
972113 is prime. b^((n-1)/972113)-1 mod n = 196216934, which is a unit, inverse 80765271.
(972113) divides n-1.
(972113)^2 > n.
n is prime by Pocklington's theorem.