Primality proof for n = 36753053:

Take b = 2.

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

2963 is prime.
b^((n-1)/2963)-1 mod n = 8206146, which is a unit, inverse 9036392.

443 is prime.
b^((n-1)/443)-1 mod n = 9672133, which is a unit, inverse 29300467.

(443 * 2963) divides n-1.

(443 * 2963)^2 > n.

n is prime by Pocklington's theorem.