Primality proof for n = 32061889897:

Take b = 2.

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

1335912079 is prime.
b^((n-1)/1335912079)-1 mod n = 16777215, which is a unit, inverse 20490923712.

(1335912079) divides n-1.

(1335912079)^2 > n.

n is prime by Pocklington's theorem.