Primality proof for n = 2843:
Take b = 2.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 1338, which is a unit, inverse 1430.
7 is prime.
b^((n-1)/7)-1 mod n = 1657, which is a unit, inverse 501.
(7^2 * 29) divides n-1.
(7^2 * 29)^2 > n.
n is prime by Pocklington's theorem.