**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) ...