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.