Primality proof for n = 8995256861:

Take b = 2.

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

3623 is prime.
b^((n-1)/3623)-1 mod n = 6419724765, which is a unit, inverse 6319943534.

2887 is prime.
b^((n-1)/2887)-1 mod n = 3551853849, which is a unit, inverse 3923286623.

(2887 * 3623) divides n-1.

(2887 * 3623)^2 > n.

n is prime by Pocklington's theorem.