arXiv subjects

Madieyna Diouf

Publications and source records attributed to Madieyna Diouf.

6 recordsLinked to original sources

arXiv2024

Improving the error term in the sieve of Eratosthenes

We have devised an alternative approach to sifting integers in the sieve of Eratosthenes that helps refine the error term. Instead of eliminating all multiples of a prime number $p<z$ in the traditional sieve method, our approach solely eliminates multiples of $p$ that have the minimum prime factor of $p$. By leveraging the density of integers with the least prime factor $p$ in this sieve technique, we obtain a reduced error term and an upper bound of $π(x)$ that accurately reflects the prime number theorem.

math.GM↗

arXiv2021

On the Distribution of Twin Primes

We introduce a sieve for counting twin primes up to a given range. Our method depends on a parameter $λ_x$ and the estimation of the number of twin primes obtained as a result, is called a fundamental structure of the distribution of twin primes. Combining the latter with an asymptotic bound of $λ_x$, establishes venues, conducive to a discovery of a partial result that can be considered as a suitable variant of the prime number theorem. Furthermore, we obtain an asymptotic bound of the number of twin primes less than $x$.

math.GM↗

arXiv2020

The gap $g_n$ between two consecutive primes satisfies $g_n=O({p_n}^{2/3})$

The following is proven using arguments that do not revolve around the Riemann Hypothesis or Sieve Theory. If $p_n$ is the $n^{\rm th}$ prime and $g_n=p_{n+1}-p_n$, then $g_n=O({p_n}^{2/3})$.

math.NT↗

arXiv2019

A conditional proof of Legendre's Conjecture and Andrica's conjecture

The Legendre conjecture has resisted analysis over a century, even under assumption of the Riemann Hypothesis. We present, a significant improvement on previous results by greatly reducing the assumption to a more modest statement called the Parity conjecture. Let $p_n$ and $p_{n+1}$ be two consecutive odd primes, let $m$ be their midpoint fixed once for all. Conjecture: The largest multiple of $p_n$ not exceeding ${m_i}^2$ is odd for every integer $m_i$ in the interval $(p_n, m]$. Main result: We prove that the Parity conjecture implies Legendre's conjecture and Andrica's conjecture.

math.GM↗

arXiv2017

Prime-Generating Polynomial

We present a prime-generating polynomial $(1+2n)(p -2n) + 2$ where $p>2$ is a lower member of a pair of twin primes less than $41$ and the integer $n$ is such that $\: \frac {1-p}{2} < n < p-1$.

math.GM↗

arXiv2017

On the prime counting function and the partial sum of reciprocals of odd primes

We present a function that tests for primality, factorizes composites and builds a closed form expression of $π(n^2)$ in terms of $\sum_{3 \leq p \leq n} \frac{1}{p}$ and a weaker version of $ω(n)$.

math.GM↗