Primality proof for n = 208147:

Take b = 2.

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

307 is prime.
b^((n-1)/307)-1 mod n = 131184, which is a unit, inverse 148445.

113 is prime.
b^((n-1)/113)-1 mod n = 31827, which is a unit, inverse 13178.

(113 * 307) divides n-1.

(113 * 307)^2 > n.

n is prime by Pocklington's theorem.