Primality proof for n = 1601:

Take b = 3.

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

5 is prime.
b^((n-1)/5)-1 mod n = 441, which is a unit, inverse 167.

2 is prime.
b^((n-1)/2)-1 mod n = 1599, which is a unit, inverse 800.

(2^6 * 5^2) divides n-1.

(2^6 * 5^2)^2 > n.

n is prime by Pocklington's theorem.