Primality proof for n = 5336643803:

Take b = 2.

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

13037 is prime.
b^((n-1)/13037)-1 mod n = 545201552, which is a unit, inverse 3693013844.

4177 is prime.
b^((n-1)/4177)-1 mod n = 832831245, which is a unit, inverse 5315758707.

(4177 * 13037) divides n-1.

(4177 * 13037)^2 > n.

n is prime by Pocklington's theorem.