Distribution of two equidistant prime numbers - Ke, Guanguan (Nanyang Technological University, 2024)
This final-year project delves into the analysis of prime number distributions with specific intervals between them. Extensive literature reviews explore established theorems and conjectures in the field. Computational investigations are conducted to scrutinize prevalent conjectures, with a particular focus on the First Hardy-Littlewood Conjecture. A novel approach is introduced to establish a connection between the First Hardy-Littlewood Conjecture and the Upper Incomplete Gamma Function, aiming to propose an alternative expression for the conjecture. The exploration of this novel methodology forms a significant component of this project. Finally, the project includes discussions on the significance and various applications of prime numbers, elucidating their importance in diverse areas of mathematics and beyond.