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.