Take b = 2.

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

1783 is prime.

b^((n-1)/1783)-1 mod n = 83694588, which is a unit, inverse 83082399.

1571 is prime.

b^((n-1)/1571)-1 mod n = 44616513, which is a unit, inverse 64313901.

(1571 * 1783) divides n-1.

(1571 * 1783)^2 > n.

n is prime by Pocklington's theorem.