On The Infinitude of the Twin Primes

2019/09/17 by Gensel, Berndt
#2010: 11A41 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1909.07975

Abstract

We present a novel approach to the Twin Prime Conjecture, basing on the 6x ± 1 representation of primes. By defining so-called twin prime generators x ∈ \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 \mcA_n, where the maximal possible prime divisor of 6x ± 1 is fixed. Within each \mcA_n, we apply the sieve to estimate the number of generator candidates that escape all local obstructions. Due to the 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.

Related

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• A Positive Lower Bound for the Sum of Log-Reciprocal Twin Prime Products via Weighted Sieve
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