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.