Take b = 2.

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

269 is prime.

b^((n-1)/269)-1 mod n = 77876, which is a unit, inverse 63006.

11 is prime.

b^((n-1)/11)-1 mod n = 98956, which is a unit, inverse 57311.

(11 * 269) divides n-1.

(11 * 269)^2 > n.

n is prime by Pocklington's theorem.