Would this be an easier way to prove the twin prime conjecture?

Question

Prove: For every prime, $p\geq7$, there exists some $pn$ such that $p$ is its largest prime factor, $n$ is a positive integer, and $(pn-4, pn-2)$ is a twin prime.

My questions:

1. Would this indeed prove the twin prime conjecture if found to be true? If you say no, why not?
2. Would this perhaps be a simpler method than what is currently being done?
3. How would one go about proving this to be true?