Primality proof for n = 4603:

Take b = 2.

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

59 is prime.
b^((n-1)/59)-1 mod n = 1537, which is a unit, inverse 4028.

13 is prime.
b^((n-1)/13)-1 mod n = 2103, which is a unit, inverse 4174.

(13 * 59) divides n-1.

(13 * 59)^2 > n.

n is prime by Pocklington's theorem.