Primality proof for n = 4481:

Take b = 3.

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

7 is prime.
b^((n-1)/7)-1 mod n = 1590, which is a unit, inverse 4450.

5 is prime.
b^((n-1)/5)-1 mod n = 474, which is a unit, inverse 917.

2 is prime.
b^((n-1)/2)-1 mod n = 4479, which is a unit, inverse 2240.

(2^7 * 5 * 7) divides n-1.

(2^7 * 5 * 7)^2 > n.

n is prime by Pocklington's theorem.