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.