On Existence of Prime K-Tuples Conjecture for Positive Proportion of Admissible K-Tuples

Authors

Ashish Mor, Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, India.Follow
Surbhi Gupta, Department of Mathematics, Amity Institute of Applied Sciences, Amity University, Noida, India.Follow

Abstract

Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The significance of this result is that it is unconditional which means it is proved without assuming any form of strong conjecture like the Elliott–Halberstam conjecture

Keywords

Admissible, Positive Proportion, Primes, Prime k-tuples, Prime k-tuples conjecture, Unsolved conjectures

Article Type

Article

How to Cite this Article

Mor, Ashish and Gupta, Surbhi (2024) "On Existence of Prime K-Tuples Conjecture for Positive Proportion of Admissible K-Tuples," Baghdad Science Journal: Vol. 21: Iss. 3, Article 18.
DOI: https://doi.org/10.21123/bsj.2023.8635