Primality proof for n = 10399:

Take b = 2.

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

1733 is prime.
b^((n-1)/1733)-1 mod n = 63, which is a unit, inverse 7758.

(1733) divides n-1.

(1733)^2 > n.

n is prime by Pocklington's theorem.