Primality proof for n = 3201858007053309020095208815543:

Take b = 2.

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

533643001175551503349201469257 is prime.
b^((n-1)/533643001175551503349201469257)-1 mod n = 63, which is a unit, inverse 2541157148455007158805721282177.

(533643001175551503349201469257) divides n-1.

(533643001175551503349201469257)^2 > n.

n is prime by Pocklington's theorem.