Primality proof for n = 929:

Take b = 3.

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

29 is prime.
b^((n-1)/29)-1 mod n = 346, which is a unit, inverse 733.

2 is prime.
b^((n-1)/2)-1 mod n = 927, which is a unit, inverse 464.

(2^5 * 29) divides n-1.

(2^5 * 29)^2 > n.

n is prime by Pocklington's theorem.