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.