Oh sure, I do agree that if you know there are FINITELY many primes that eliminate all pairs, then it is obvious that there must be one that eliminates the remaining twin primes.For there not to be infinitely many twin primes, it takes one and only one prime to do away with all the remaining 6n-1 and 6n+1 pairs ahead of it. I will prove this statement which I thought would be quite obvious to those who just do a little bit of thinking about it. Since we are dealing with infinitely many 6n-1 and 6n+1 pairs, is it not obvious that if the twin primes are finite then only one prime is needed to eliminate all the infinite number of un-eliminated 6n-1 and 6n+1 pairs? It will be absurd to say 5 primes for instance will be needed to collectively eliminate the 6n-1 and 6n+1 pairs because that will mean that the first of the 5 primes did not remove all the 6n-1 and 6n+1 pairs and similarly the second, third and fourth did not remove all the 6n-1 and 6n+1 pairs. It will be the fifth prime that will achieve this i.e. one and only one prime will be required to render the twin prime conjecture false. We are in agreement from previous posts that no prime can do this and so the twin prime conjecture is true, no doubt.

But there are an infinite number of primes. So how do you know that there are finitely many primes that eliminate all pairs?

And, I know we're stupid people. But if you give somebody a proof to get feedback on, and they ask a question, don't reply with saying it's obvious five times. It's just insulting. I don't care, but journals will.

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