The Riemann Hypothesis, a cornerstone in number theory, illuminates prime number distribution’s average and the deviations from this mathematical norm. Originating in Riemann’s seminal 1859 paper, it posits that the elusive zeros of the zeta function inhabit the complex plane with a real part fixed at 1/2. This hypothesis offers a one-million-dollar challenge for those capable of providing a valid proof in a respected mathematical journal. Remarkably, a parallel emerges when considering the shared challenges between the Riemann Hypothesis and the domain of medical predictions, where accurate outcome forecasting remains a formidable task in intricate scenarios. Stephen Wolfram’s Principle of Computational Equivalence underscores the computational essence of complex processes. Within this concise communication, we delve into two conjectures related to the generalized Riemann Hypothesis for Dirichlet L-functions, transcending disciplinary boundaries to intertwine elements of number theory, medical science, and captivating references such as Abraham Lincoln and a hypothetical set of dogs with cardinality one.

In this paper, we challenge the conventional wisdom surrounding prime numbers and their infinite nature, diverging from the Riemann hypothesis. We argue that prime numbers are, in fact, finite entities with profound implications for number theory. Our investigation reveals inherent flaws in number theory's applicability to the real number line, which comprises an infinite continuum between whole numbers. We explore the connection to modular mathematics, highlighting the topological constraints on number division, ultimately leading to the neglect of the historical significance of whole numbers. Furthermore, we propose a novel perspective on the relationship between prime numbers and the fundamental principles of physics, particularly in the context of general relativity calculus. We assert that spacetime itself may be composed of prime number multiples of particle pairs, providing a solution to the potential consequences of forces acting with an infinite finitude through self-division. This paper challenges conventional mathematical and physical paradigms, offering a fresh perspective on the finite nature of prime numbers and its far-reaching implications for our understanding of the universe.

Amazing…..? Negative and positive sum of prime number are equal…very interesting …please see this working so beautiful. New conjectures in number theory I think

The “strong Goldbach conjecture” posits that any even number exceeding 6 can be represented as the sum of two prime numbers. This study explores this hypothesis, leveraging the constancy of odd integer quantities and cumulative sums within positive integers. By identifying odd prime numbers, pα1 and pα2, within [3, n] and (n, 2n-2) intervals, we demonstrate a transformative process grounded in the unchanging nature of odd number counts and their cumulative sums. Through this process, we establish the equation 2n =pα1 + pα2, offering a significant stride in unraveling the enigmatic core of the strong Goldbach conjecture.

Within this paper, we embark on a comprehensive exploration of the profound scientific issues intertwined with the concept of the infinite within the realm of natural numbers. Through meticulous analysis, we delve into three distinct perspectives that shed light on the nature of natural number infinity. By considering the framework of time reference, we confront and address the inherent challenges that arise when contemplating the infinite. Furthermore, we navigate the intricate relationship between the infinite and fundamental scientific questions, seeking to unveil novel insights and resolutions. In a departure from conventional viewpoints, our examination of natural number infinity takes on a relativistic dimension, scrutinizing the role of time and the observer's perspective. Strikingly, as we delve deeper into the foundational strata, we uncover the pivotal significance of relativity not only in physics but also in mathematics. This realization propels us towards a more holistic and consistent mathematical framework, underlining the inextricable link between the infinitude of natural numbers and the essential constructs of time and perspective.

This paper presents a proof of the Collatz conjecture for a specific subset of positive integers, those formed by multiplying a prime number ”p” greater than three with an odd integer ”u” derived using Fermat’s little theorem. Additionally, we introduce a novel screening criterion for identifying candidate twin primes, extending our previous work linking twin primes (p and p+2) with the equation 2(p−2) = pu+v, where unique solutions for u and v are required. This unified criterion offers a promising approach to twin prime identification within a wider range of integers, further advancing research in this mathematical domain

I am developing a novel technique for evaluating the behavior of math students, which holds potential benefits for teachers, professors, and school educators. This innovative approach aims to enhance the understanding of student behavior in the context of mathematics learning. Traditionally, assessing student behavior has been a subjective and time-consuming process. However, this new technique incorporates advanced methodologies to capture and analyze various behavioral aspects. By leveraging technology and data-driven insights, educators can gain a deeper understanding of how students engage with mathematical concepts, their problem-solving approaches, and their overall learning attitudes.

Unbelievable is make believable in the world we connected prime number in matrix algebra form and I change history of math. Please see it

This paper introduces a novel approach to estimating the distribution of of prime numbers by leveraging insights from partition theory, prime number gaps, and the angles of triangles. Application of this methodology to infinite sums and the nth sum, and propose several ways of defining the nth sum of a prime number By using the Ramanujan infinite series of natural numbers. I will be able to derive an infinite series of prime numbers.