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On The Infinitude of the Twin Primes

On The Infinitude of the Twin Primes

来源:Arxiv_logoArxiv
英文摘要

We present a novel approach to the Twin Prime Conjecture, basing on the $6x \pm 1$ representation of primes. By defining so-called twin prime generators $x \in \N$, for which both $6x - 1$ and $6x + 1$ are prime, we reformulate the conjecture into the existence problem of such $x$. Using admissible residue classes modulo products of small primes and an adapted Selberg sieve, we partition the natural numbers into structured intervals $\mc{A}_n$, where the maximal possible prime divisor of $6x \pm 1$ is fixed. Within each $\mc{A}_n$, we apply the sieve to estimate the number of generator candidates that escape all local obstructions. Due to the \emph{parity problem} we cannot solve the problem with a Selberg sieve. It requires other sieves or methods. The author is searching for them and invites all interested people to help.

Berndt Gensel

数学

Berndt Gensel.On The Infinitude of the Twin Primes[EB/OL].(2025-08-18)[2025-08-23].https://arxiv.org/abs/1909.07975.点此复制

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