Take b = 2.

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

89 is prime.

b^((n-1)/89)-1 mod n = 1152977, which is a unit, inverse 2200779.

41 is prime.

b^((n-1)/41)-1 mod n = 2631218, which is a unit, inverse 3872863.

(41 * 89) divides n-1.

(41 * 89)^2 > n.

n is prime by Pocklington's theorem.