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LANGUAGE LIMITATIONS - I looked through the language standard a bit, and the only thing I found was that the size-specifier in the brackets must evaluate to a "constant integral value". If I understand that correctly, you should be able to use an unsigned long int, which can hold values up to 4,294,967,295. (4 bytes).

I'm afraid you don't understand that correctly. Integral doesn't mean it has to be of type int, integral refers to any number evenly divisible by 1 in general. That's where all the ints get their name. If that was the limit, I'm sure it would've been specified in more direct terms.