Primality test challenge

And we begin with very simple question ? or not a question a challenge. We need to build a machine which takes an input and that input is some integer x and all that machine needs to do is to put true(T) or false(F) and that is the first step now we will use computer science to actually build this machine together and one of the questions that we will be asking is two things two aspects to this machine how much time thats a clock how much time does it take to give solution ? and how much space doest it need ? and when i say space i mean in case of mechanical calculator physical space how many rooms do we need to hold our machine ? or for using a computer how much memory does it need ? so we will be retaining to these two ideas as we go...