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.