Primality proof for n = 6247:

Take b = 2.

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

347 is prime.
b^((n-1)/347)-1 mod n = 6016, which is a unit, inverse 5625.

(347) divides n-1.

(347)^2 > n.

n is prime by Pocklington's theorem.