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.