Primality proof for n = 95024118539459:

Take b = 2.

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

9801157 is prime.
b^((n-1)/9801157)-1 mod n = 74831220632818, which is a unit, inverse 40427696818302.

(9801157) divides n-1.

(9801157)^2 > n.

n is prime by Pocklington's theorem.