Primality proof for n = 900886289:
Take b = 2.
b^(n-1) mod n = 1.
27109 is prime.
b^((n-1)/27109)-1 mod n = 407331351, which is a unit, inverse 614376904.
67 is prime.
b^((n-1)/67)-1 mod n = 26234084, which is a unit, inverse 259062632.
(67 * 27109) divides n-1.
(67 * 27109)^2 > n.
n is prime by Pocklington's theorem.