Primality proof for n = 962161:
Take b = 2.
b^(n-1) mod n = 1.
211 is prime.
b^((n-1)/211)-1 mod n = 342513, which is a unit, inverse 852476.
19 is prime.
b^((n-1)/19)-1 mod n = 540313, which is a unit, inverse 212940.
(19 * 211) divides n-1.
(19 * 211)^2 > n.
n is prime by Pocklington's theorem.