Take b = 2.

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

1049 is prime.

b^((n-1)/1049)-1 mod n = 3102586, which is a unit, inverse 3095100.

277 is prime.

b^((n-1)/277)-1 mod n = 78115, which is a unit, inverse 846644.

(277 * 1049) divides n-1.

(277 * 1049)^2 > n.

n is prime by Pocklington's theorem.