Primality proof for n = 6917:
Take b = 2.
b^(n-1) mod n = 1.
19 is prime.
b^((n-1)/19)-1 mod n = 4063, which is a unit, inverse 3633.
13 is prime.
b^((n-1)/13)-1 mod n = 1746, which is a unit, inverse 5162.
(13 * 19) divides n-1.
(13 * 19)^2 > n.
n is prime by Pocklington's theorem.