title: Proof that there only exists exactly 4 factorion numbers?
body: <p>I've having difficulty understanding why 40585 is the greatest factorion that exists. Why can there not be one greater? </p>
  
  <p><a href="http://en.wikipedia.org/wiki/Factorion" rel="nofollow">Wikipedia</a> says, "This fails to hold for d ≥ 8." In other words no factorion can exist with more than 7 digits. </p>
  
  <p>But how is this known? How can it be proven? What about for very very large numbers, perhaps one that has not yet been tested?</p>