Application of Odd Pairs of Partitions of an Even Number of a New Formulation in Validating the Twin Prime Conjecture

The Twin Prime Conjecture posits the existence of infinitely many pairs of prime numbers (p, p + 2), where both p and p + 2 are prime. Despite centuries of investigation, a definitive proof remains elusive. Prime numbers, defined by their indivisibility except by one and themselves, display an apparently erratic distribution. Researchers have utilized a combination of theoretical insights, computational analysis, and innovative mathematical techniques in their quest to solve this conjecture. However, the unpredictable nature of prime occurrences has kept this problem open in Number Theory. This study introduces a novel approach involving the partitioning of even numbers into pairs of odd numbers. We demonstrate that within the set of all such pairs, there exists a proper subset that includes all prime numbers. Notably, this proper subset consistently contains at least two prime numbers differing by 2, providing a potential pathway to validating and proving the Twin Prime Conjecture.