is operator works confusingly with integers

  • integer
  • is
  • operator

Why does the following behave unexpectedly in Python?

>>> 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