Primality proof for n = 84869:

Take b = 2.

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

433 is prime.
b^((n-1)/433)-1 mod n = 50133, which is a unit, inverse 1830.

(433) divides n-1.

(433)^2 > n.

n is prime by Pocklington's theorem.