Primality proof for n = 95338435633553477:

Take b = 2.

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

522528103 is prime.
b^((n-1)/522528103)-1 mod n = 16095092816155858, which is a unit, inverse 70180366529673081.

(522528103) divides n-1.

(522528103)^2 > n.

n is prime by Pocklington's theorem.