For example, how can I use the result of 1000^1000 for arithmetic? I don\'t think there\'s a library that can accommodate that, all I see at most is 100 number digits.
What you are looking for is a library like GMP or Boost-Multiprecision or TTmath.
Or, you might challenge yourself to write a low level representation that handles longer than standard bit representations, and do arithmetic with it.
Stick with the first option though, if it does the job you have in mind.