Primality proof for n = 2939:

Take b = 2.

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

113 is prime.
b^((n-1)/113)-1 mod n = 2676, which is a unit, inverse 2492.

(113) divides n-1.

(113)^2 > n.

n is prime by Pocklington's theorem.