Primality proof for n = 858239144413883:
Take b = 2.
b^(n-1) mod n = 1.
326257 is prime.
b^((n-1)/326257)-1 mod n = 736392267752739, which is a unit, inverse 405260866868181.
71471 is prime.
b^((n-1)/71471)-1 mod n = 725394242153382, which is a unit, inverse 189798240383950.
(71471 * 326257) divides n-1.
(71471 * 326257)^2 > n.
n is prime by Pocklington's theorem.