Primality proof for n = 5849:
Take b = 2.
b^(n-1) mod n = 1.
43 is prime.
b^((n-1)/43)-1 mod n = 3764, which is a unit, inverse 3616.
17 is prime.
b^((n-1)/17)-1 mod n = 3077, which is a unit, inverse 3682.
(17 * 43) divides n-1.
(17 * 43)^2 > n.
n is prime by Pocklington's theorem.