Primality proof for n = 3863568481:

Take b = 2.

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

8049101 is prime.
b^((n-1)/8049101)-1 mod n = 3393365178, which is a unit, inverse 1639958190.

(8049101) divides n-1.

(8049101)^2 > n.

n is prime by Pocklington's theorem.