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.