Generating very large random numbers in c++

I'm working with an algorithm and would like to do some statistics on it with some very large random numbers. I would like the numbers generated to come from the interval [2^255, 2^256], but it would be equivalent to generate a number in [0,2^255].

I'm working in C++ but I'm very new to programming and only know the basics. Is this even a plausible thing to do (in terms of memory and computing power)? I've seen other posts dealing with 2^32 and 2^64, but haven't found anything quite this big. The only computations I'll be doing with these numbers are comparison, division, and subtraction.

If so, how would I write the code to accomplish such a task?