Primality proof for n = 29179:
Take b = 2.
b^(n-1) mod n = 1.
1621 is prime. b^((n-1)/1621)-1 mod n = 28711, which is a unit, inverse 23630.
(1621) divides n-1.
(1621)^2 > n.
n is prime by Pocklington's theorem.