Take b = 2.

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

181 is prime.

b^((n-1)/181)-1 mod n = 85749, which is a unit, inverse 54941.

5 is prime.

b^((n-1)/5)-1 mod n = 63674, which is a unit, inverse 101435.

(5 * 181) divides n-1.

(5 * 181)^2 > n.

n is prime by Pocklington's theorem.