Primality proof for n = 22709:

Take b = 2.

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

811 is prime.
b^((n-1)/811)-1 mod n = 15075, which is a unit, inverse 10825.

(811) divides n-1.

(811)^2 > n.

n is prime by Pocklington's theorem.