A Novel Computational Verification of Goldbach's Conjecture up to 10^15 Using the N/2 Prime Ladder Method

Goldbach's Conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers. This paper introduces the "N/2 Prime Ladder Method", a new computational approach to verify the conjecture. Instead of checking all prime pairs, this method starts from N/2 and moves outward in a "ladder" fashion, significantly reducing computation time. An open-source web tool was developed to implement this method and has successfully verified all even numbers up to 10^15. This work provides strong computational evidence for the conjecture and introduces an efficient algorithm for future large-scale verification.