If you have in x some very large number, like 3**200000, then the computation for 'str(x)' is sub-efficient.  Nathan Hurst posted to the pypy-dev mailing list a pure Python algo that gives the same result in 2/3rd of the time (in either CPython or PyPy).  We would get a similar gain by recoding this algorithm in C.

The mail is here: http://mail.python.org/pipermail/pypy-dev/2013-May/011433.html