Take b = 2.

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

53 is prime.

b^((n-1)/53)-1 mod n = 26896162, which is a unit, inverse 75712971.

29 is prime.

b^((n-1)/29)-1 mod n = 68236645, which is a unit, inverse 100085220.

7 is prime.

b^((n-1)/7)-1 mod n = 95730223, which is a unit, inverse 4923006.

(7 * 29 * 53) divides n-1.

(7 * 29 * 53)^2 > n.

n is prime by Pocklington's theorem.