Primality proof for n = 213095137:

Take b = 2.

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

3529 is prime.
b^((n-1)/3529)-1 mod n = 35019268, which is a unit, inverse 17407833.

37 is prime.
b^((n-1)/37)-1 mod n = 206800799, which is a unit, inverse 142562166.

(37 * 3529) divides n-1.

(37 * 3529)^2 > n.

n is prime by Pocklington's theorem.