clearly has to be odd, so is an integer.
Then
is clearly greater than 1; if you can show that then you’re done ( would be the product of two integers greater than one and so can’t be prime).
Okay, here we go. Prove that for all odd integers .
First, check the cases and separately.
For odd integers , I claim that . This can be proved by a slight variation of the method of induction.
When , .
Suppose for some odd integer .
Now consider . (NB: is the next odd integer.)
*
*
Hence, for all odd integers , and it follows that .