Primality proof for n = 85999:

Take b = 2.

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

1303 is prime.
b^((n-1)/1303)-1 mod n = 11851, which is a unit, inverse 14107.

(1303) divides n-1.

(1303)^2 > n.

n is prime by Pocklington's theorem.