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[15] viXra:2405.0159 [pdf] replaced on 2025-08-26 01:37:04
Authors: Jim Rock
Comments: 3 Pages.
In 1742 Christian Goldbach suggested that any even number four or greater is the sum of two primes.The Goldbach conjecture remains unproven to the present day, although it has been verified for all even numbers up to 4 × 10^18. Previously this problem has been attacked using deep analytical methods and with complicated integer sieves. This paper takes an entirely new approach to the Goldbach conjecture using pairs of composite integers (composite pairs) that are used to find pairs of prime numbers (prime airs) that sum to the same even natural number.
Category: Number Theory
[14] viXra:2405.0129 [pdf] replaced on 2024-08-22 19:54:47
Authors: Abdelmajid Ben Hadj Salem
Comments: 5 Pages. Submitted to the Czechoslovak Mathematical Journal. Comments welcome.
In this paper, we consider the abc conjecture. Assuming the conjecture c
Category: Number Theory
[13] viXra:2405.0114 [pdf] submitted on 2024-05-22 15:53:46
Authors: Juan Elias Millas Vera
Comments: 2 Pages.
I share some thoughts about prime number and the use of basis in number theory.
Category: Number Theory
[12] viXra:2405.0112 [pdf] submitted on 2024-05-21 12:00:22
Authors: Lance Horner
Comments: 1 Page.
We relate the product of the vertices of a regular n-gon in the complex plane to the nth powers of the n-gon's center and complex radii.
Category: Number Theory
[11] viXra:2405.0099 [pdf] submitted on 2024-05-18 20:27:02
Authors: Pawel Piskorz
Comments: 3 Pages.
We propose a procedure which allows to compute the only acceptable natural exponents of the positive integers X, Y, Z in the equation of the Fermat’s Last Theorem. We use the approach similar to the one applied in computing of the expected value and the standard deviation of number of successes in Bernoulli trials presented by Kenneth S. Miller.
Category: Number Theory
[10] viXra:2405.0078 [pdf] submitted on 2024-05-15 13:35:37
Authors: Ricardo Gil
Comments: 3 Pages.
The Riemann Hypothesis proposes a specific location (the critical line) for the non-trivial zeros of the Riemann zeta function. This paper argues that the aperiodicity observed in the distribution of these non-trivial zeros and the distribution of primes numbers is a fundamental property. A periodic zeta function would significantly alter its behavior, rendering it irrelevant to studying prime number distribution. Conversely, a periodic pattern in prime numbers or a deviation of non-trivial zeros from the critical line would disprove the Riemann Hypothesis. The observed aperiodicity in both prime number distribution and the zeta function's non-trivial zeros strengthens the case for the Hypothesis' validity. This aperiodicity suggests a deeper connection between prime numbers and the zeta function, one that wouldn't exist with a periodic structure.
Category: Number Theory
[9] viXra:2405.0070 [pdf] submitted on 2024-05-14 22:07:32
Authors: Geon Cho
Comments: 2 Pages. (Correction made by viXra Admin to conform with the requirements of viXra.org - Future non-compliant submission will not be accepted)
This paper attempts a simple proof for the Fermat’s Last Theorem.
Category: Number Theory
[8] viXra:2405.0062 [pdf] submitted on 2024-05-11 20:25:56
Authors: Massimo Russo
Comments: 10 Pages.
With the right equipment and a specially developed algorithm, I believe that my function could potentially find the largest prime number ever, even one with billions of digits. It might even be possible to find two or more consecutive prime numbers each with billions of digits.
Category: Number Theory
[7] viXra:2405.0048 [pdf] replaced on 2024-07-07 22:29:50
Authors: John Yuk Ching Ting
Comments: 31 Pages. Finalized Preprint Version for submission to JNT dated July 7, 2024.
From perspective of Number theory, Dirichlet eta function (proxy function for Riemann zeta function as generating function for all nontrivial zeros) and Sieve of Eratosthenes (as generating algorithm for all prime numbers) are essentially infinite series. We apply infinitesimals to their outputs. Riemann hypothesis asserts the complete set of all nontrivial zeros from Riemann zeta function is located on its critical line. It is proven to be true when usefully regarded as an Incompletely Predictable Problem. We ignore even prime number 2. The complete set with derived subsets of Odd Primes all contain arbitrarily large number of elements while satisfying Prime number theorem for Arithmetic Progressions, Generic Squeeze theorem and Theorem of Divergent-to-Convergent series conversion for Prime numbers. Having these theorems satisfied by all Odd Primes, Polignac's and Twin prime conjectures are separately proven to be true when usefully regarded as Incompletely Predictable Problems.
Category: Number Theory
[6] viXra:2405.0035 [pdf] submitted on 2024-05-07 21:00:49
Authors: Zhiyang Zhang
Comments: 8 Pages.
This paper classifies non trivial zeros based on the Riemann Zeta function. Through this operation, we can clearly understand the distribution pattern of non trivial zeros and predict the position of the next zero point. You can know that the Riemann hypothesis has three types of non trivial zeros, and the first type of non trivial zeros is located on the critical line, while the second and third types of zeros are not. Meanwhile, through a series of equation derivations, we can also understand why it is so difficult to find counterexamples of the Riemann hypothesis.
Category: Number Theory
[5] viXra:2405.0033 [pdf] submitted on 2024-05-07 20:48:11
Authors: Viktor Strohm
Comments: 6 Pages. (Converted to pdf and author name added by viXra admin - Please only submist article in pdf format)
This paper reveals/discusses the connection between the difference of prime numbers and the remainder of division by 6, the periodicity of the remainder.
Category: Number Theory
[4] viXra:2405.0032 [pdf] submitted on 2024-05-07 19:09:34
Authors: Edgar Valdebenito
Comments: 5 Pages.
Motzkin numbers have many combinatorial interpretations. In particular, M(n) is the total number of ways in which it is possible to draw non-intersecting chords between n points on a circle.
Category: Number Theory
[3] viXra:2405.0024 [pdf] submitted on 2024-05-05 20:53:41
Authors: Toshiro Takami
Comments: 6 Pages.
I proved the Twin Prime Conjecture by using Clement’s theorem. I was able to transform below. (n is positive integer) 4×(6n − 2)! + 6n + 3 ≡ 0 (mod (6n − 1)(6n + 1)). Even if the number(n) reaches the limit, use n=x+1,n=x+2...n=x+18 from n=x. By n=x+18, new twin prime numbers are found.In this way, even larger twin primes are born.Repeat this. That is, Twin Primes exist forever.
Category: Number Theory
[2] viXra:2405.0006 [pdf] submitted on 2024-05-03 00:01:32
Authors: Mostafa Senhaji
Comments: 24 Pages. In French
Delve into the fascinating depths of conjectureof Syracuse through this captivating work. Of its humble beginnings with complex ramifications, explore a mathematical problem that captured the imagination of researchers for decades. Discover the first empirical observations which led to the formulation ofthe conjecture, as well as the various attempts to solve, from classical approaches to modern methods. But the Syracuse conjecture is not limited to its mathematical aspects. Explore his connections with others fields of science, from cryptography to the theory of information, through musical analogy and geometric representations. At each step, discovernew ways this simple conjecture can illuminate complex concepts in other areas. This book offers an in-depth exploration of theSyracuse conjecture, combining mathematical rigor and creative imagination. It also offers aformal demonstration of convergence towards 1 for all initial value, thus consolidating our understanding of this intriguing phenomenon. Whether you are a researcher seasoned or passionate about mathematics, let yourselfinspire and challenge through this journey through a problem that continues to captivate the minds of the world's entire mathematicians.
Category: Number Theory
[1] viXra:2405.0004 [pdf] replaced on 2024-05-09 08:40:14
Authors: Rolando Zucchini
Comments: 11 Pages.
With reference to the Syracuse Conjecture Quadrature (SCQ), this article contains two links of high main horizons and their corresponding lower horizons such that Ꝋ(l) < Ꝋ(m), calculated by Theorem of Independence. A further confirmation that cycles of links can be managed to our liking. Moreover the procedure explains show the beauty and the magical harmony of odd numbers. At the same time it’s confirmed that SC (or CC) is not fully verifiable as additional highlighted by the four illustrative patterns. There are no doubts: it’s a particular sort of the Circle Quadrature, but its initial statement is true. In other words: BIG CRUNCH (go back to 1) is always possible but BIG BANG (to move on) has no End.
Category: Number Theory
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