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.