# Proof of twin prime conjecture

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#### [email protected]

So his uniqueness argument is not merely unproven, but unprovable and unnecessary. ROFL
Problem is, you can't convince him of this, since he argues by contradiction...

You can come up with a different kind of algebraic structure where there are provably finitely many twin primes, and show his argument fails there. Or you can do like collag3n above and consider teta-primes to show his argument fails. But he doesn't understand those, so he will dismiss it.

By the way, you might be interested in a simple proof of Bael's conjecture, also very hilarious: The Simple Proof of Beal's Conjecture - xkcd

#### Collag3n

You are all making a very simple explanation of the truth of the twin prime conjecture over complicated probably because the maths gurus like Field medalist, Terence Tao have made the twin prime conjecture a big deal when really it is not. My proof is just as logical and as simple as proving the infinitude of primes. My proof uses the sieve of Eratosthenes, which by the way is the algorithmic generator of the primes, to show the infinitude of twin primes. I have shown that the sieve of Eratosthenes cannot 'hit' all the 6n-1 and 6n+1 pairs using a simple proof. This sieve operates by giving every prime greater than 3 opportunities to eliminate 6n-1 and 6n+1 pairs. It is agreed that each prime in its infinite hopping will hop over an infinite number of un-eliminated 6n-1and 6n+1 pairs and therefore no one prime can eliminate all infinite number of 6n-1 and 6n+1 pairs. This means that the twin primes will never run out.

Read my post top of page 5 (if you didn't catch the flaw in the previous post I made): none of my teta-primes can eliminates all teta-twins (they eliminate a infinitely small portion of them at each step), there are still an infinite of teta-twins at each step but in the end, there is NO teta-twin at all. NONE !!!! But the reasoning is exactly the one you have. Can you explain why ? (this is basic math, no need to be Terence)

#### [email protected]

Read my post top of page 5 (if you didn't catch the flaw in the previous post I made): none of my teta-primes can eliminates all teta-twins (they eliminate a infinitely small portion of them at each step), there are still an infinite of teta-twins at each step but in the end, there is NO teta-twin at all. NONE !!!! But the reasoning is exactly the one you have. Can you explain why ? (this is basic math, no need to be Terence)
Smart argument! But don't bother, the OP won't understand the relevance of your example. He's been pushing this exact proof for 9 years already Proof of the Twin Prime Conjecture - xkcd

#### Collag3n

At least I Tried

Ok, look again at my sieve (top of page 5). There is no way any of my teta-prime can eliminate all teta-twins. They NEVER RUN OUT like you say. At each step and forever, despite the infinite number of teta-multiples sieved, there will be infinitely many teta-twin candidates left.

You would think there are infinitely many teta-twins. Nonetheless I dare you to give me 1 (only 1) example of teta-twin that will never be sieved.

#### MrAwojobi

I don't see how you can formulate an entirely different problem and begin to draw an analogy to my twin prime proof. In fact, come to think of it, I can dispense with all my talk about if the twin prime conjecture is false, it will take one and only one special prime to eliminate all the 6n-1 and 6n+1 pairs at some point in its elimination process. This has been the main statement that a lot of you have been hanging on to. I still believe in this statement but it doesn't even need to be in the proof because the mere fact that every prime, 5 or greater, will perpetually keep hopping over un-eliminated 6n-1 and 6n+1 pairs during its turn on the number line with all multiples of 2 and 3 removed is enough to prove the twin prime conjecture is true. Every prime having this property means that these pairs can never run out. No one, as yet, has come up with a way that these pairs can run out apart from one prime doing the job if this was possible. All you keep doing is formulating new problems and trying to use analogical arguments. That doesn't work for me. Stick to this twin prime problem at hand and explain if there is any other way for all these pairs to be eliminated at some point if the twin prime conjecture is false. None of you can because there is no other way i.e. if the twin prime conjecture is false. A fraction of infinity is a lesser infinity but still infinity. With my way that fraction of infinity is 1. This means that this prime takes out all the infinity number of pairs and not say a third or half or a quarter of infinity. Of course this latter part of my discussion is based on if the twin prime conjecture is false. I don't need to read some difficult philosophical books about infinity by the 'Greats' to come up with my own common sense concept of infinity.

#### topsquark

Math Team
I don't need to read some difficult philosophical books about infinity by the 'Greats' to come up with my own common sense concept of infinity.
Common sense is a good thing to have. It leads us to interesting areas of Math. However common sense is trumped by proof. You say that there will always be pairs 6n - 1 and 6n + 1 that will not be "sieved out" but you offer no proof of this statement. As we have been saying all along.

It's nice when it happens but not everything is provable using High School level Math. Read some of those Philosophy texts. You might learn something there.

-Dan

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