Primality proof for n = 208150935158385979:

Take b = 2.

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

191039911 is prime.
b^((n-1)/191039911)-1 mod n = 89709188498985665, which is a unit, inverse 133855595432530999.

3023 is prime.
b^((n-1)/3023)-1 mod n = 178020065538317617, which is a unit, inverse 70005499209399486.

(3023 * 191039911) divides n-1.

(3023 * 191039911)^2 > n.

n is prime by Pocklington's theorem.