Prime Number Principle

This essay evolved from reading the chapter on George Sands' Prime Number Principle in Arthur F. MacTier's new book Card Concepts (Lewis Davenport, 2000). For those who don't know, here's Sands' effect in brief begin with a prime number of cards P 3, 5, 7, 11, or 13, Note the top card. Pick any number N less than the number of cards in the packet. Transfer N cards from top to bottom, then turn over the top card. Do this P-1 times in total. The card noted will be the only card remaining...