Primality proof for n = 208469:
Take b = 2.
b^(n-1) mod n = 1.
211 is prime.
b^((n-1)/211)-1 mod n = 3834, which is a unit, inverse 115218.
19 is prime.
b^((n-1)/19)-1 mod n = 100400, which is a unit, inverse 3262.
(19 * 211) divides n-1.
(19 * 211)^2 > n.
n is prime by Pocklington's theorem.