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.