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.