Proof that if x is prime, then x+7 is composite.

Question

Proof that if x is prime, then x+7 is composite.
I do not know how to prove it. Can anyone help me to solve it? Thx

Answer 1

Simple.

If some number is prime,then it must be odd.Sum of two odd numbers is even,thus sum of any prime and odd number is even number.Even numbers are never prime(except 2),since they are divisible by 2.

Since x is prime then x+7 is not prime,due to lemma given above

Unless x=2,which is prime,but 2+7 is 9 ,which is composite.

Answer 2

If $x = 2$, then $x + 7 = 9$ and so composite.

Else, $x$ is odd. So $x + 7$ is even, and so composite.