Primality proof for n = 4451:

Take b = 2.

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

89 is prime.
b^((n-1)/89)-1 mod n = 3832, which is a unit, inverse 2301.

(89) divides n-1.

(89)^2 > n.

n is prime by Pocklington's theorem.