Fastest way in C# to iterate through ALL Guids Possible

EDIT I know this might sound stupid, but please stop voting the question down. The point has been made. No need to keep voting it down. In fact, Im pretty sure this is the most negative votes for any SO question ever.

I have access to one of the top 50 fastest computers in the world. This question I am trying to complete is for a job that is required to get done. While it might not make sense on an ordinary regular computer in the civilized world, it makes sense to do it with the hardware and capabilities I have. Please understand, that this will be done, it just depends on how fast.

As the title says.

I have made a console application to count all iterations of a Guid. That is 2^128 times.

I want to start with 00000000000000000000000000000000 and end with the iteration of fffffffffffffffffffffffffff.

Is this the fastest way to do so? Im looking for help on the most efficient code possible, just because I know it will take forever and a day to get done.

Im looking for any and all help to speed this puppy up.

WHY You Ask?

I am screen scraping web content. Sadly, the web content was not put in integer format from 0-999999. But it was actually formatted with Guids instead. I want to hit all the guids on the site to see if there is content that resides there.

Here is my main program.

static void Main(string[] args)
    {
        Console.WriteLine("Guid to start");
        string start = Console.ReadLine();

        string start1 = "00000000000000000000000000000000";
        string iteration = start;

        using (StreamWriter outfile = new StreamWriter(@"c:\temp\scanner\guids.txt"))
        {
            for (Double k = 0; k < 5316911983139663491615228241121400000d; k++)
            {
                Console.WriteLine(site + iteration + extension);
                outfile.WriteLine(iteration);
                iteration = NextLetter(iteration);

                try
                {//do work on the Guid
                }
                catch
                {
                    outfile.WriteLine("broke");
                    Console.WriteLine("broke");
                }
                                }
            outfile.Close();
            Console.ReadLine();
        }
    }

Here is the method to increment the Guid.

        public static string NextLetter(string letter)
    {
        const string alphabet = "abcdefghijklmnopqrstuvwxyz0123456789";
        if (!string.IsNullOrEmpty(letter))
        {
            char lastLetterInString = letter[letter.Length - 1];

            // if the last letter in the string is the last letter of the alphabet
            if (alphabet.IndexOf(lastLetterInString) == alphabet.Length - 1)
            {
                //replace the last letter in the string with the first leter of the alphbat and get the next letter for the rest of the string
                return NextLetter(letter.Substring(0, letter.Length - 1)) + alphabet[0];
            }
            else
            {
                // replace the last letter in the string with the proceeding letter of the alphabet
                return letter.Remove(letter.Length - 1).Insert(letter.Length - 1, (alphabet[alphabet.IndexOf(letter[letter.Length - 1]) + 1]).ToString());
            }
        }
        //return the first letter of the alphabet
        return alphabet[0].ToString();
    }