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.