Expressing Even Numbers Beyond 6 as Sums of Two Primes

The “strong Goldbach conjecture” posits that any even number exceeding 6 can be represented as the sum of two prime numbers. This study explores this hypothesis, leveraging the constancy of odd integer quantities and cumulative sums within positive integers. By identifying odd prime numbers, pα1 and pα2, within [3, n] and (n, 2n-2) intervals, we demonstrate a transformative process grounded in the unchanging nature of odd number counts and their cumulative sums. Through this process, we establish the equation 2n =pα1 + pα2, offering a significant stride in unraveling the enigmatic core of the strong Goldbach conjecture.