The datetime class provides a min datetime object which is not formattable:

on Python 2:

$ python
Python 2.7.3 (default, Apr 10 2013, 05:13:16) 
[GCC 4.7.2] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import datetime
>>> datetime.datetime.min.strftime('%Y')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: year=1 is before 1900; the datetime strftime() methods require year >= 1900
>>> 

and on Python 3:

$ python3
Python 3.2.3 (default, Apr 10 2013, 05:07:54) 
[GCC 4.7.2] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> import datetime
>>> datetime.datetime.min.strftime('%Y')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: year=1 is before 1000; the datetime strftime() methods require year >= 1000
>>>

It seems to me that either datetime.datetime.min.year should be increased to 1900/1000 or strftime should be able to format year=1 - it is strange that the API doesn't support its own constants.

works correctly on python3.3:
Python 3.3.2 (default, Oct  4 2013, 12:21:07)
[GCC 4.2.1 20070831 patched [FreeBSD]] on freebsd9
Type "help", "copyright", "credits" or "license" for more information.
>>> import datetime
>>> datetime.datetime.min.strftime('%Y')
'0001'

issue on 2.7:
Python 2.7.5 (default, Sep 17 2013, 12:11:31)
[GCC 4.2.1 20070831 patched [FreeBSD]] on freebsd9
Type "help", "copyright", "credits" or "license" for more information.
>>> import datetime
>>> datetime.datetime.min.strftime('%Y')
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: year=1 is before 1900; the datetime strftime() methods require year >= 1900

Indeed, this is already fixed.  This issue is a duplicate of issue 1777412.  The bug will not be fixed in earlier versions for the reasons discussed in that issue.