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.