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.