Primality proof for n = 95959:

Take b = 2.

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

1777 is prime.
b^((n-1)/1777)-1 mod n = 62719, which is a unit, inverse 11660.

(1777) divides n-1.

(1777)^2 > n.

n is prime by Pocklington's theorem.