Primality proof for n = 85831:

Take b = 2.

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

2861 is prime.
b^((n-1)/2861)-1 mod n = 81844, which is a unit, inverse 38061.

(2861) divides n-1.

(2861)^2 > n.

n is prime by Pocklington's theorem.