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.