Primality proof for n = 6197:
Take b = 2.
b^(n-1) mod n = 1.
1549 is prime. b^((n-1)/1549)-1 mod n = 15, which is a unit, inverse 2892.
(1549) divides n-1.
(1549)^2 > n.
n is prime by Pocklington's theorem.