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.