Primality proof for n = 999964351:

Take b = 2.

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

28859 is prime.
b^((n-1)/28859)-1 mod n = 912634493, which is a unit, inverse 946804165.

11 is prime.
b^((n-1)/11)-1 mod n = 928179583, which is a unit, inverse 145452734.

(11 * 28859) divides n-1.

(11 * 28859)^2 > n.

n is prime by Pocklington's theorem.