On the Collatz Conjecture

Solving Collatz Conjecture could bring instant happiness to your life... Fine, maybe not happiness, but approximately $1,000,000.00 based on my estimates of how famous you'll be.

Let's start with the conjecture, then we'll talk more:

prove that the code below always ends for any positive integer

Professor Collatz came up with this conjecture when he was only 22 years old, in 1932, while working on some graph construction problems. He himself made no progress in solving it. Almost 100 years later, and still very little progress has been made. It is one of the simplest open problems in modern mathematics, and yet one for which mathematicians have little to no clue on how to even begin to tackle it.
I wrote the code below to calculate it (also known as "the 3x+1 conjecture"), and using BigIntegers, you can try really big numbers. No matter how large you try, as far as I know, it always stops....
Cheers, ACC.

Collatz.exe 12332112332112332112332112332112332112332112332112332112332112332112332112332112332112332112332112344321

A.: 2434

using System;

using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

namespace Collatz
{
    class Program
    {
        static void Main(string[] args)
        {
            BigInteger n = BigInteger.Parse(args[0]);
            Console.WriteLine(_Collatz(n));
        }

        static int _Collatz(BigInteger n)
        {
            return (n == 1) ? 0 : (1 + _Collatz(n % 2 == 0 ? n / 2 : 3 * n + 1));
        }
    }
}