The Twin Primes Conjecture is a long standing problem in mathematics as to whether there are infinitely many pairs of primes with a difference of 2. This page is home to 2 related but different proofs of the problem.

In 2016 I devised a proof that involved scanning lines and parabolas across hyperbolas, and then showing that a certain parabola that always generated twins had infinite solutions. It was written very hastily and informally, as I was only then becoming familiar with using Latex for the write up.

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About 2 years later I came up with a revised version that no longer used the scanning, but used 2 surfaces instead. While the concept was sound, and much easier to follow than the first, the proof was not rigorous enough for certain portions of its claims. The first proof had lead to the second, but both relied on a claim about the natural values of 2 surfaces either being or not being a basis for the set of odd numbers, or all the natural numbers, respectively.

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Then in 2020, I was able to explicitly show all the steps and logic of the 2nd attempt. The paper presented here is a consolidation of all my attempts and work on the subject into a single resource. It was a massive overhaul to the explanation of the original proof, and a quality of life revision to the later.

You can download the pdf here, or view it in the tiles below, and it can also be found on vixra, here. https://vixra.org/pdf/2009.0086v2.pdf

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If you would like to discuss the work further, suggest improvements, or find any errors, please contact me..

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