C# SMTP Server ansprechen mislingt, warum?

Hallo, ich programiere an einem SMTP client und versuche mein Account 
bei gmx.net anzusprechen.

Per Telnet geht es sehr gut:

c:\telnet mail.gmx.net 25

220 mail.gmx.net GMX Mailservices ESMTP {mp010}
quit
221 2.0.0 GMX Mailservices {mp010}

Connection to host lost.

Das gleiche versche ich programatisch zu machen aber es gibt den
folgenden Fehler in der
ersten Zeile(TcpClient mailclient = new TcpClient("mail.gmx.net", 25);)

Fehler:

A connection attempt failed because the connected party did not properly 
respond after a period of time, or established connection failed because 
connected host has failed to respond.


Hat jemand bitte eine Idee?








Hier ist das Program:

using System;
using System.Text;
using System.Text.RegularExpressions;
using System.Net;
using System.Net.Sockets;
using System.Threading;
using System.IO;
using System.Collections.Generic;
using System.Collections.ObjectModel;

namespace connect
{

    public class test
    {
        static void Main(string[] args)
        {

            TcpClient mailclient = new TcpClient("mail.gmx.net", 25);
            NetworkStream mailstream = mailclient.GetStream();
            StreamReader mailreader = new StreamReader(mailstream);
            StreamWriter mailwriter = new StreamWriter(mailstream);
            mailwriter.NewLine = "\r\n";
            mailwriter.AutoFlush = true;

            string mailline;

            do
            {
              mailline = mailreader.ReadLine();
            } while (!mailline.StartsWith("220 "));
            Console.WriteLine(mailline);
            mailwriter.WriteLine("QUIT");
            mailclient.Close();


        }

    }

}