Primality proof for n = 5743:
Take b = 2.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 900, which is a unit, inverse 3784.
11 is prime.
b^((n-1)/11)-1 mod n = 4051, which is a unit, inverse 4219.
(11 * 29) divides n-1.
(11 * 29)^2 > n.
n is prime by Pocklington's theorem.