Well, the Manhattan project is a good example of something that remained secret from the public for far longer than any formula would predict, given the gigantic amount of people involved (though of course other state actors knew about it long before).
I guess it depends on your definition of "remained secret from the public". For example, Kodak figured it out pretty quickly after the first tests because the radiation particles in the atmosphere were carried from the Southwest US to their factories in Rochester, NY, and affected their film production.
