>     public static int? LargestPrime(int max)
>     {
>         if (max < 0)
>             return null;
>         int largestPrime = 0;
>         for (int i = 0; i <= max; i++)
>         {              
>             bool? isPrime = IsPrime(i);
>             if ((bool)isPrime)
>                 largestPrime = i;
>             if (i % 100000 == 0)
>                 Console.WriteLine(largestPrime.ToString("N0"));
>         }
>         return largestPrime;
>     }  

- Omitting braces `{}`, although they might be optional, won't do you good in the long run because it makes your code error-prone.  

- If an argument of a method isn't correct like `max < 0` you should throw either an `ArgumentException` or better an `ArgumentOutOfRangeException`.  

- You are iterating from `0` to `max` to check if the value is a prime, but I wonder what else could the number be? Either it is a prime or it isn't a prime, there is no third way so it doesn't make sense that `IsPrime()` returns a nullable bool.  

___  

### bool? IsPrime(int n)  

Here you are iterating from `5` to `i*i<n` for each number which is passed to the method.   

So let us assume that we pass `max = 10.000.000` (the dots are there for clearity) this  

>         if (n % i == 0 || n % (i + 2) == 0)
>             return false;

in the `for` loop in the `IsPrime()` method is executed `16.194.513` times.

By using a sieve you could pretty much speed this thing up like so  

    static int CalculateLargestPrime(int maxPrime)
    {
        bool[] isComposite = new bool[maxPrime + 1];
        for (int x = 2; x * x <= maxPrime; x++)
        {
            if (!isComposite[x])
            {
                for (int y = x * x; y <= maxPrime; y = y + x)
                {
                    isComposite[y] = true;
                }
            }
        }
        for (int i = maxPrime; i >= 0; i--)
        {
            if (!isComposite[i])
            {
                return i;
            }
        }

        return -1;
    }  

taken and adjusted from https://codereview.stackexchange.com/a/62158/29371