Primality proof for n = 963926494829235139921:

Take b = 2.

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

880691887 is prime.
b^((n-1)/880691887)-1 mod n = 940251452989926706616, which is a unit, inverse 335737063190318778704.

198280883 is prime.
b^((n-1)/198280883)-1 mod n = 653784643977091094325, which is a unit, inverse 166622018899174174028.

(198280883 * 880691887) divides n-1.

(198280883 * 880691887)^2 > n.

n is prime by Pocklington's theorem.