Primality proof for n = 921589:

Take b = 2.

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

1259 is prime.
b^((n-1)/1259)-1 mod n = 687365, which is a unit, inverse 781126.

(1259) divides n-1.

(1259)^2 > n.

n is prime by Pocklington's theorem.