Primality proof for n = 9533836766459662372116970697:

Take b = 2.

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

1191729595807457796514621337 is prime.
b^((n-1)/1191729595807457796514621337)-1 mod n = 255, which is a unit, inverse 5309038513087341399374940545.

(1191729595807457796514621337) divides n-1.

(1191729595807457796514621337)^2 > n.

n is prime by Pocklington's theorem.