Primality proof for n = 4847597:

Take b = 2.

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

101 is prime.
b^((n-1)/101)-1 mod n = 2933042, which is a unit, inverse 2555285.

71 is prime.
b^((n-1)/71)-1 mod n = 3104481, which is a unit, inverse 1423939.

(71 * 101) divides n-1.

(71 * 101)^2 > n.

n is prime by Pocklington's theorem.