Primality proof for n = 18947:

Take b = 2.

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

9473 is prime.
b^((n-1)/9473)-1 mod n = 3, which is a unit, inverse 6316.

(9473) divides n-1.

(9473)^2 > n.

n is prime by Pocklington's theorem.