  We present an elementary proof of the prime number theorem. The relative
error follows a golden ratio scaling law and respects the bound obtained from
the Riemann's hypothesis. The proof is derived in the framework of a scale free
nonarchimedean extension of the real number system exploiting the concept of
relative infinitesimals introduced recently in connection with ultrametric
models of Cantor sets. The extended real number system is realized as a
completion of the field of rational numbers $Q$ under a {\em new}
nonarchimedean absolute value, which treats arbitrarily small and large numbers
separately from a finite real number.
