c# singleton class working well confirmation

Question

I need a confirmation about a singleton pattern.

I've a singleton class and I'm using it as dll. I write a program with a reference to this dll and I call my singleton class. I write a second program and I do the same.

Am I right if I tell you that even if I have two program they call both a single instance of my singleton class?

I tried to increment an static variable instancenumber that increment each time I pass the constructor and both programs tell me that the instancenumber is 1. So it should be ok but I need your advice to be sure.

Thank you. best regards

Class Singleton:

namespace SingletonClassLib
{
    public class SingletonClass
    {
        public static int InstanceNumber = 0;
        private static string myName;
        #region //Singleton initialisation
        private SingletonClass() { createInstance(); }
        private void createInstance()
        {
            InstanceNumber++;
            myName = myName + InstanceNumber.ToString();
        }
        public static SingletonClass _I { get { return NTCSession._i; } }
        private class NTCSession
        {
            static NTCSession() { }
            internal static readonly SingletonClass _i = new   SingletonClass();
        }
        private static List<WeakReference> instances = new List<WeakReference>();
        #endregion //Singleton initialisation
        public static string askname { get { return myName; } }
    }
    }

Program 1:

using System.Windows.Forms;
using SingletonClassLib;

namespace Singletontest
{

public partial class Form1 : Form
{
    SingletonClass myclass = SingletonClass._I;
    public Form1()
    {
        InitializeComponent();
        string Name = SingletonClass.askname;
        MessageBox.Show("Program first: "+Name);
    }
}
}

Program 2:

using System.Windows.Forms;
using SingletonClassLib;

namespace Singletontest
{

public partial class Form1 : Form
{
    SingletonClass myclass = SingletonClass._I;
    public Form1()
    {
        InitializeComponent();
        string Name = SingletonClass.askname;
        MessageBox.Show("Program second: "+Name);
    }
}
}

Answer 1

As other answers suggest, the singleton instance is not shared between the two programs. Each program runs in its own OS process that has its own DLL copy