Primality proof for n = 858397:

Take b = 2.

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

929 is prime.
b^((n-1)/929)-1 mod n = 730925, which is a unit, inverse 575387.

(929) divides n-1.

(929)^2 > n.

n is prime by Pocklington's theorem.