Primality proof for n = 671065561:

Take b = 2.

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

991 is prime.
b^((n-1)/991)-1 mod n = 159542748, which is a unit, inverse 539399916.

19 is prime.
b^((n-1)/19)-1 mod n = 74316606, which is a unit, inverse 647427994.

11 is prime.
b^((n-1)/11)-1 mod n = 90255800, which is a unit, inverse 125939268.

(11 * 19 * 991) divides n-1.

(11 * 19 * 991)^2 > n.

n is prime by Pocklington's theorem.