1) has to be greater than 1 !
If is prime we are done, so let's assume that is not prime. Then for some . If is prime, we are done. If this is not so, then for some that is
Now repeat this process. We can ensure it will end since after steps we get and this doesn't hold for large enough .
This proves that at some point is going to be prime. (since this ends if and only if is prime) .And we are done.
2). Simple note that is even, ( so if k>0 then it is a number greater than 2 and divisible by it, hence not prime). is multiple of 3, so it only can be prime if it is 3 itself. (again even) ...