Primality proof for n = 4871:

Take b = 2.

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

487 is prime.
b^((n-1)/487)-1 mod n = 1023, which is a unit, inverse 2176.

(487) divides n-1.

(487)^2 > n.

n is prime by Pocklington's theorem.