>>>> the data type does not need any arithmetic operations (as of integers).
You arguably do not have a number but simply a string that looks like a number. Other examples are zip-codes and phone-numbers if you ignore symbols. Thus you should probably use an appropriately sized char/varchar.
Just something to consider; there is no hard and fast rule about this kind of thing. If you can think of any logical use of arithmetic operators, even if you do not need them now, you should use an integer.
Dave