Pré-Publication, Document De Travail Année : 2018

The Twin Prime Conjecture

Résumé

Consecutive primes which differ only by two are known as twin primes; the function $\pi_2(x)$ describes the distribution of the twin primes in the set of natural numbers. The twin prime conjecture states that there are infinitely many primes $p$ such that $p + 2$ is also prime. At the present time, the knowledge about twin primes comes mostly from sieve methods. Using a formulation of the sieve of Eratosthenes supported on a sequence of $k$-tuples of remainders we obtain a lower bound for the number of twin primes in $[1, x]$. Thus, we prove that $\pi_2(x) \to \infty$ as $x \to \infty$.

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Dates et versions

hal-01882333 , version 1 (26-09-2018)
hal-01882333 , version 2 (13-11-2020)
hal-01882333 , version 3 (24-08-2023)

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  • HAL Id : hal-01882333 , version 3

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Ricardo Guillermo Barca. The Twin Prime Conjecture. 2018. ⟨hal-01882333v3⟩
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