private constructor

A private constructor is a special instance constructor. It is generally used in classes that contain static members only. If a class has one or more private constructors and no public constructors, other classes (except nested classes) cannot create instances of this class. 
For example:

public class Counter
{
    private Counter() { }
    public static int currentCount;
    public static int IncrementCount()
    {
        return ++currentCount;
    }
}

class TestCounter
{
    static void Main()
    {
        // If you uncomment the following statement, it will generate 
        // an error because the constructor is inaccessible: 
        // Counter aCounter = new Counter();   // Error

        Counter.currentCount = 100;
        Counter.IncrementCount();
        Console.WriteLine("New count: {0}", Counter.currentCount);

        // Keep the console window open in debug mode.
        Console.WriteLine("Press any key to exit.");
        Console.ReadKey();
    }
}
// Output: New count: 101

 When we declare a class constructor as private , we can not do 2 things:-

1. We can not create a object of the class.
2. We can not inherit the class.