Primality proof for n = 29611:
Take b = 2.
b^(n-1) mod n = 1.
47 is prime.
b^((n-1)/47)-1 mod n = 18053, which is a unit, inverse 22353.
5 is prime.
b^((n-1)/5)-1 mod n = 22691, which is a unit, inverse 8434.
(5 * 47) divides n-1.
(5 * 47)^2 > n.
n is prime by Pocklington's theorem.