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.