While reading popular science book Fermat's Last Theorem I was amazed to find out that in number theory interesting things happen even at very large scales. For instance the Graham's number was named "the largest number ever used in a serious mathematical proof", but this is quite rare (is it?) and it seems that lot of the "interesting" numbers are located not far from zero (Should I say in the middle of the number line? Or at the center of the complex plane?)
I am not a mathematician, I don't even know how to ask the right thing and my question can be closed as off topic. But I hope someone will understand what I mean and reply with interesting thoughts or recommended reading.
So, what is the "shape" of numbers in Number Theory?