Take b = 2.

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

61 is prime.

b^((n-1)/61)-1 mod n = 10466, which is a unit, inverse 4234.

29 is prime.

b^((n-1)/29)-1 mod n = 5482, which is a unit, inverse 1469.

(29 * 61) divides n-1.

(29 * 61)^2 > n.

n is prime by Pocklington's theorem.