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.