Use of Private Constructor in C#

Private constructors are used to prevent creating instances of a class when there are no instance fields or methods, such as the Math class, or when a method is called to obtain an instance of a class. If all the methods in the class are static, consider making the complete class static.   Sealed class cannot be inherited but it can be instantiated. On the other hand, a class having a private constructor neither can be inherited nor instantiated due to its protection level

• Classes containing only static methods
• Singletons
• Factory Design patterns
  most common example is singleton pattern
• 
  
  using System; public sealed class Test { public static readonly Test Instance = new Test(); // Singleton pattern public int A; // Instance field private Test() // This is the private constructor { this.A = 5; } } class Program { static void Main() { // We can access an instance of this object that was created. // ... The private constructor was used. Test test = Test.Instance; // These statements show that the class is usable. Console.WriteLine(test.A); test.A++; Console.WriteLine(test.A); } } Output 5 6
  Check this
  http://www.dotnetperls.com/private-constructor