A Reflective Examination of Even Integers and Prime Pair Decompositions in Goldbach?s Conjecture

Abhijit Manohar

Abstract: The discussion revisits Goldbach?s conjecture by outlining a numerical approach that expresses every even integer as the sum of two prime numbers through relationships based on the form 6k plus or minus 1. The analysis shows how pairs of constants can be used to generate corresponding primes for any even value by drawing on the structure of integers within modular classes. Examples from small values and extended ranges, including even numbers between 1000 and 1100, demonstrate how specific combinations of k and k' yield valid prime pairs. The argument is supported by broader computational work that has explored the conjecture up to very large magnitudes, reinforcing the view that even integers consistently align with prime pair representations within this framework.

Keywords: Goldbach conjecture, prime numbers, Leonhard Euler, even integers

How to Cite?: Abhijit Manohar, "A Reflective Examination of Even Integers and Prime Pair Decompositions in Goldbach?s Conjecture", Volume 14 Issue 12, December 2025, International Journal of Science and Research (IJSR), Pages: 219-220, https://www.ijsr.net/getabstract.php?paperid=SR251201104107, DOI: https://dx.doi.org/10.21275/SR251201104107