Primality proof for n = 41201:

Take b = 3.

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

103 is prime.
b^((n-1)/103)-1 mod n = 16838, which is a unit, inverse 17121.

5 is prime.
b^((n-1)/5)-1 mod n = 18548, which is a unit, inverse 26467.

(5^2 * 103) divides n-1.

(5^2 * 103)^2 > n.

n is prime by Pocklington's theorem.