Primality proof for n = 5859383:

Take b = 2.

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

30203 is prime.
b^((n-1)/30203)-1 mod n = 62169, which is a unit, inverse 679820.

(30203) divides n-1.

(30203)^2 > n.

n is prime by Pocklington's theorem.