Number Theory

2401 Submissions

[16] viXra:2401.0153 [pdf] replaced on 2024-03-06 08:45:15

Pythagorean Triples and Fermat's Theorem N = 4

Authors: Rolando Zucchini
Comments: 7 Pages.

This article contains a theorem to build the Primitive Pythagorean triples and the proof of the last Fermat’s Theorem for n = 4.
Category: Number Theory

[15] viXra:2401.0132 [pdf] submitted on 2024-01-26 18:00:12

Periodic Function Approach to Prime Number Analysis with Graphical Illustrations

Authors: Budee U. Zaman
Comments: 15 Pages.

This paper introduces a novel approach employing periodic functions for the comprehensive analysis of prime numbers. The method ncompassesprimality testing, factor counting and listing, prime distribution calculation, and the determination of the Nth prime. The exposition of the technique is presented in a clear and sequential manner, guiding the reader through each step with explicit equations. Graphs are strategically incorporated between crucial stages to facilitate a rapid and intuitive visualization of the rationale and outcomes of each maneuver. The paper concludes with concise reflections and ongoing inquiries into the potential applications and refinements of the proposed method.
Category: Number Theory

[14] viXra:2401.0122 [pdf] submitted on 2024-01-24 20:12:56

Rsa 2048 Factoring NPQ

Authors: Ricardo Gil
Comments: 5 Pages.

The purpose of this paper is to provide an algorithm that has 5 lines of code and that finds P & Q when N is given. It will work for RSA 2048 & RSA-617.
Category: Number Theory

[13] viXra:2401.0104 [pdf] submitted on 2024-01-21 22:03:34

The Riemann Hypothesis Has no Counterexamples When Imaginary Part Below One Million Billion

Authors: Zhiyang Zhang
Comments: 2 Pages.

This article aims to identify counterexamples of the Riemann hypothesis. Although no upper bound was found for the counterexample, at least it was proven that there were no counterexamples when imaginary part below one million billion, significantly increasing the lower bound of the counterexample.
Category: Number Theory

[12] viXra:2401.0091 [pdf] submitted on 2024-01-21 01:01:32

Continued Fraction Generalization [Part 3]

Authors: Isaac Mor
Comments: 18 Pages.

This is a list of ten types of continued fraction generalization. (This is [Part 3] , every volume contains 10 formulas) I am using Euler's continued fraction formula in order to find some nice continued fraction generalization.
Category: Number Theory

[11] viXra:2401.0087 [pdf] submitted on 2024-01-20 00:56:23

A Simple Proof of The ABC Conjecture

Authors: Oussama Basta
Comments: 3 Pages.

This work analyzes the ABC conjecture, which states that for any positive real number ε, there exists a constant Kε such that for all coprime positive integer triples (a, b, c) with a + b = c, c < Kε * rad(abc)^(1 + ε). We focus on the case where a > F, F > ε, and b = (a + F - ε), c = (a + F + ε), where F and ε are positive real numbers with F > ε.
Category: Number Theory

[10] viXra:2401.0084 [pdf] replaced on 2024-01-22 17:58:56

Riemann Hypothesis: Direct Demonstration Proposal

Authors: Vincent KOCH
Comments: 3 Pages.

In his 1859 article "On the number of prime numbers less than a given quantity", Bernhard Riemann formulated the hypothesis that all non-trivial zeros of the Zeta function have the real part 1/2.This assertion, known as the "Riemann Hypothesis", remains unproven to this day. The present paper is an attempt at a direct demonstration.
Category: Number Theory

[9] viXra:2401.0081 [pdf] submitted on 2024-01-16 23:55:05

Hypothesis: Distribution of Primes and the Logarithmic Expression

Authors: Anil Sharma
Comments: 4 Pages.

This research explores the distribution of prime numbers using a novel ljogarithmic expression. The hypothesis suggests that an expression, partitions natural numbers into groups, revealing a systematic distribution of primes. Experimental results demonstrate an intriguing pattern as the range of N increases, with the average number of primes in each group stabilizing around 15. The paper discusses thebackground, mathematical expression, experimental results, and potentialavenues for future research.
Category: Number Theory

[8] viXra:2401.0072 [pdf] submitted on 2024-01-16 01:10:42

Revolutionizing Prime Factorization: A Time Complexity-Optimized Approach for Efficient Composite Number Analysis

Authors: Anil Sharma
Comments: 2 Pages.

This research investigates patterns in prime number distributions and proposes an optimized factorization method. A novel approach is introduced to explore the position of the first prime factor in composite numbers, focusing on a specific range for potential computational time savings.
Category: Number Theory

[7] viXra:2401.0068 [pdf] replaced on 2024-01-19 20:47:42

A Convergent Subsequence of $theta_n(x+iy)$ in a Half Strip

Authors: Young Deuk Kim
Comments: 8 Pages. Typos are fixed.

For $frac{1}{2}0$ and $ninmathbb{N}$, let $displaystyletheta_n(x+iy)=sum_{i=1}^nfrac{{mbox{sgn}}, q_i}{q_i^{x+iy}}$,where $Q={q_1,q_2,q_3,cdots}$ is the set of finite product of distinct odd primes and${mbox{sgn}}, q=(-1)^k$ if $q$ is the product of $k$ distinct primes.In this paper we prove that there exists an ordering on $Q$ such that $theta_n(x+iy)$ has a convergent subsequence.
Category: Number Theory

[6] viXra:2401.0064 [pdf] submitted on 2024-01-13 21:07:52

An Efficient Method to Prove that the Riemann Hypothesis Is Not Valid

Authors: Zhiyang Zhang
Comments: 12 Pages. (Name added to article by viXra Admin - Please conform!)

Analytical number theory is a combination of trigonometric functions and polynomial symbols, which can be solved no matter how difficult it is. Therefore, I believe that the Riemann hypothesis is not unsolvable. In the field of number theory, the mathematical community tends to seek a maximum number to overturn the conclusion. Whether it is the Riemann hypothesis or the Goldbach conjecture, this should be the solution.
Category: Number Theory

[5] viXra:2401.0054 [pdf] submitted on 2024-01-13 04:07:31

On the Sum of Reciprocals of Primes

Authors: Young Deuk Kim
Comments: 5 Pages.

Suppose that $y>0$, $0leqalpha<2pi$ and $0K$ and $P^-$ the set of primes $p$ such that $cos(yln p+alpha)<-K$ . In this paper we prove $sum_{pin P^+}frac{1}{p}=infty$ and $sum_{pin P^-}frac{1}{p}=infty$.
Category: Number Theory

[4] viXra:2401.0046 [pdf] submitted on 2024-01-09 21:34:50

Redefining Mathematical Structure: From the Real Number Non-Field to the Energy Number Field

Authors: Parker Emmerson
Comments: 8 Pages.

The traditional classification of real numbers (R) as a complete ordered field is contested throughcritical examination of the field axioms, with a focus on the absence of a multiplicative inverse for zero. We propose an alternative mathematical structure based on Energy Numbers (E), deriving from quantum mechanics, which addresses the classical anomalies and fulfills field properties universally, including an element structurally analogous but functionally distinctive from the zero in R.
Category: Number Theory

[3] viXra:2401.0018 [pdf] submitted on 2024-01-04 20:18:27

Charles Hutton's Formula

Authors: Edgar Valdebenito
Comments: 3 Pages.

Some remarks about a formula of Charles Hutton.
Category: Number Theory

[2] viXra:2401.0009 [pdf] submitted on 2024-01-02 04:44:33

Contribution to Goldbach's Conjectures

Authors: Radomir Majkic
Comments: 6 Pages.

The internal structure of the natural numbers reveals the relation between the weak and strong Goldbach's conjectures. Explicitly, if the weak Goldbach's conjecture is true, the strong Goldbach's conjecture is, and Goldbach's conjectures are true.
Category: Number Theory

[1] viXra:2401.0008 [pdf] replaced on 2024-01-23 01:28:41

Goldbach's Number Construction

Authors: Radomir Majkic
Comments: 7 Pages.

The internal structure of the natural numbers reveals the relation between the weak and the strong Goldbach's conjectures. The three prime integers structure of the odd integers alreadycontains the two prime integers base of the even integers. An explicit one-to-one correspondence between these two structures, defined asGoldbach's numbers exist. Thus, if the weak Goldbach's conjecture is true, the strong Goldbach'sconjecture should be. Hopefully, this will bring a happy end to Goldbach'sconjecture problem.
Category: Number Theory