An Exploratory Observation on Representing Even Numbers Using the Largest Prime Less than the Number

Sahil Kumar, Braham Pal Singh

Abstract: This paper examines an observational approach related to the Strong Goldbach Conjecture, which states that every even integer greater than 2 can be expressed as the sum of two prime numbers or prime and 1. The study explores a heuristic method based on selecting the largest prime number less than a given even integer and analyzing the difference between the two values. Several numerical examples are presented to illustrate this pattern. The results show that, in many cases, subtracting the largest prime less than the given even number yields another prime, supporting known empirical behavior. However, the approach does not constitute a formal proof and remains a computational observation. The study highlights limitations related to identifying large primes and suggests directions for further analytical refinement.

Keywords: Goldbach Strong Conjecture, Prime numbers, Even integers, number theory, heuristic methods