Primality proof for n = 74729:

Take b = 2.

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

9341 is prime.
b^((n-1)/9341)-1 mod n = 255, which is a unit, inverse 26668.

(9341) divides n-1.

(9341)^2 > n.

n is prime by Pocklington's theorem.