Take b = 5.

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

3 is prime.

b^((n-1)/3)-1 mod n = 362, which is a unit, inverse 263.

2 is prime.

b^((n-1)/2)-1 mod n = 575, which is a unit, inverse 288.

(2^6 * 3^2) divides n-1.

(2^6 * 3^2)^2 > n.

n is prime by Pocklington's theorem.