Primality proof for n = 9437362120201:
Take b = 2.
b^(n-1) mod n = 1.
701527 is prime.
b^((n-1)/701527)-1 mod n = 2348147931013, which is a unit, inverse 1033940864616.
3203 is prime.
b^((n-1)/3203)-1 mod n = 7848722715653, which is a unit, inverse 4334511429809.
(3203 * 701527) divides n-1.
(3203 * 701527)^2 > n.
n is prime by Pocklington's theorem.