Python - is Operator

Today I am going to explain how the is operator in python works and some weird case study with it.
From the documentation: Every object has an identity, a type and a value. An object’s identity never changes once it has been created; you may think of it as the object’s address in memory. The ‘is‘ operator compares the identity of two objects; the id() function returns an integer representing its identity (currently implemented as its address). This would seem to indicate that it compares the memory addresses of the arguments, though the fact that it says "you may think of it as the object's address in memory" might indicate that the particular implementation is not guranteed; only the semantics are. One surprising case with the is operator,

                       >>> a = 256
                       >>> b = 256
                       >>> a is b
                       True           # this is an expected result
                       >>> a = 257
                       >>> b = 257
                       >>> a is b
                       False          # what happened here? why is this False?
                       >>> 257 is 257
                       True           # yet the literal numbers compare properly
                       

                       >>> a = 256
                       >>> b = 256
                       >>> id(a)
                       9987148
                       >>> id(b)
                       9987148
                       >>> a = 257
                       >>> b = 257
                       >>> id(a)
                       11662816
                       >>> id(b)
                       11662828
                       

The current implementation keeps an array of integer objects for all integers between -5 and 256, when you create an int in that range you actually just get back a reference to the existing object. So it should be possible to change the value of 1. I suspect the behaviour of Python in this case is undefined.