A Proof of Goldbach's Conjecture Using a New Number Representation

Goldbach's Conjecture states that every even integer  can be expressed as the sum of two prime numbers. In this paper, we introduce a new approach involving an auxiliary correction term , where , to systematically establish the existence of two primes  and  satisfying . We use results from prime number distribution and Bertrand's Postulate to rigorously prove the conjecture for all even numbers.