Source : Free On-Line Dictionary of Computing

prime number theorem
     
         The number of {prime number}s less than x is
        about x/log(x).  Here "is about" means that the ratio of the
        two things tends to 1 as x tends to infinity.  This was first
        conjectured by {Gauss} in the early 19th century, and was
        proved (independently) by Hadamard and de la Vall'ee Poussin
        in 1896.  Their proofs relied on {complex analysis}, but Erdos
        and Selberg later found an "elementary" proof.
     
        (1995-04-10)