Take b = 2.

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

131 is prime.

b^((n-1)/131)-1 mod n = 44008, which is a unit, inverse 116203.

7 is prime.

b^((n-1)/7)-1 mod n = 31671, which is a unit, inverse 110168.

(7 * 131) divides n-1.

(7 * 131)^2 > n.

n is prime by Pocklington's theorem.