Primality proof for n = 961549:

Take b = 2.

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

11447 is prime.
b^((n-1)/11447)-1 mod n = 224668, which is a unit, inverse 524947.

(11447) divides n-1.

(11447)^2 > n.

n is prime by Pocklington's theorem.