Primality proof for n = 38189:
Take b = 2.
b^(n-1) mod n = 1.
9547 is prime. b^((n-1)/9547)-1 mod n = 15, which is a unit, inverse 2546.
(9547) divides n-1.
(9547)^2 > n.
n is prime by Pocklington's theorem.