A Proof of Goldbach's Strong Conjecture and the Twin Prime Conjecture

This work presents an elementary proof of the strong Goldbach conjecture and the twin prime conjecture. It establishes a rigorous lower bound on the number of representations of an even integer as a sum of two primes for all N > (2, 278, 383) ² and the lower bound density derived can be used to prove a lower bound on twin prime pairs, a bound that increases as N -> infinity. The proof shows that every even integer greater than or equal to (2, 278, 383) ² has at least one Goldbach representation. Combined with existing computational verification of the conjecture up to 4x10¹8, this result confirms the conjecture for all even integers. And the lower bound on twin prime pairs proves the twin prime conjecture. Feel free to email me at the address on the latest version with questions or feedback.