Primality proof for n = 38713:

Take b = 2.

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

1613 is prime.
b^((n-1)/1613)-1 mod n = 14486, which is a unit, inverse 17737.

(1613) divides n-1.

(1613)^2 > n.

n is prime by Pocklington's theorem.