CONTEXT: Challenge question set by uni lecturer for discrete mathematics course
Question: Prove the following statement is true using proof by contradiction:
For all positive integers $x$, if $x$, $x+2$ and $x+4$ are all prime, then $x=3$.
I know I'd do this by trying to prove the negation of the statement, but then failing to do so and hence 'contradicting' myself.
I've also found the negation to be that there exists a positive prime integer $x$ such that 𝑥+2 and 𝑥+4 are prime, but $x≠3$
I'm stuck at the part of the proof where you show that the negation is false.