Primality proof for n = 4951357:

Take b = 2.

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

8779 is prime.
b^((n-1)/8779)-1 mod n = 3478883, which is a unit, inverse 1556260.

(8779) divides n-1.

(8779)^2 > n.

n is prime by Pocklington's theorem.