Primality proof for n = 212102557441:

Take b = 2.

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

135049 is prime.
b^((n-1)/135049)-1 mod n = 199221958325, which is a unit, inverse 2061844630.

409 is prime.
b^((n-1)/409)-1 mod n = 23719261883, which is a unit, inverse 107862837290.

(409 * 135049) divides n-1.

(409 * 135049)^2 > n.

n is prime by Pocklington's theorem.