In 2016 I devised a proof that basically involved scanning lines and parabolas across hyperbolas, and showing that a certain parabola that always generated twins had infinite solutions. I still think it's valid, but the few people I tried to show had trouble following it. It was also written informally.

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About 2 years later I came up with a revised version that no longer used the scanning, but basically used 2 surfaces instead. While the concept was sound, and much easier to follow, the proof was not rigorous enough for certain portions of its claims. It was more formal than the 1st, but still not to the standards that many expect, despite it offering value and solutions.

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Then in 2020, I was able to explicitly show all the steps and logic of the 2nd attempt. It's not quite as easy to follow, but it's rigorous and much more formal.

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The 3rd one is written and posted elsewhere. All 3 should be combined in 1 nice paper, and I will try and add it or the 3rd one here soon. For now the original 2 are below, along with the descriptions I had written at that time.

A methods to prove the Twin Prime Conjecture are given and discussed. The pictures currently cover 2 short papers. First is the original proof, sufficient to convey its workings to those familiar with the topic, but written somewhat informally, and second is an update, which furthers the formalization of the logic.

The Proof works generally as follows: 1 surface is assigned to the primes such that if you choose values not on that surface you generate a prime. A 2nd surface is assigned to values 2 away from a number that are prime such that it works like the 1st surface. The proof then shows how to generate an infinite number of values that meet both surfaces criterion.

Current Status: Since the development of the technique I have sought to revise it or find a simpler version all together. Recently I have made strides in this and believe I have found a much quicker path through the logic and will add it as soon as I have time, at this point it is only on paper, not in pixels.

The status update version, not yet included, works generally as follows: Primes, except the number 2 are odd, but not composite. Numbers that are 2 greater than primes other than the number 2, and which are also prime, are odd, but not composite. An infinite number of pairs of odds that are not composites exist.

* This proof was found to have an error as stated. Most of it, and the concept behind it are still correct, it just needs fixed in one place. It was an attmept to get the same results as the original proof, but more quickly and clearly. The original is still valid, and still has had no flaws found to this date.

A methods to prove the Twin Prime Conjecture are given and discussed. The pictures currently cover 2 short papers. First is the original proof, sufficient to convey its workings to those familiar with the topic, but written somewhat informally, and second is an update, which furthers the formalization of the logic.

The Proof works generally as follows: 1 surface is assigned to the primes such that if you choose values not on that surface you generate a prime. A 2nd surface is assigned to values 2 away from a number that are prime such that it works like the 1st surface. The proof then shows how to generate an infinite number of values that meet both surfaces criterion.

Current Status: Since the development of the technique I have sought to revise it or find a simpler version all together. Recently I have made strides in this and believe I have found a much quicker path through the logic and will add it as soon as I have time, at this point it is only on paper, not in pixels.

The status update version, not yet included, works generally as follows: Primes, except the number 2 are odd, but not composite. Numbers that are 2 greater than primes other than the number 2, and which are also prime, are odd, but not composite. An infinite number of pairs of odds that are not composites exist.

Ver. 3. to be added