The Free On-line Dictionary of Computing (30 December 2018):

prime number theorem

    The number of prime numbers 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 Erdös
   and Selberg later found an "elementary" proof.

   (1995-04-10)