Primality proof for n = 38603:

Take b = 2.

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

19301 is prime.
b^((n-1)/19301)-1 mod n = 3, which is a unit, inverse 12868.

(19301) divides n-1.

(19301)^2 > n.

n is prime by Pocklington's theorem.