Goldbach's_Conjecture_Research_Paper

This research paper explores Goldbach’s Conjecture, a renowned unsolved problem in number theory, stating that every even integer greater than two can be expressed as the sum of two prime numbers. The paper provides a historical overview of the conjecture, discusses partial results such as Vinogradov’s Theorem and Chen’s Theorem, and presents computational verification of even numbers up to 100. Prime pairs are listed, patterns are observed, and graphical analysis is included to show how the number of prime pairs increases with larger even numbers. Python code used for generating the prime pairs is also provided. While the study does not prove the conjecture, it highlights trends, provides small-scale evidence supporting its validity, and illustrates how simple numerical experiments can give insight into deep mathematical questions.

This work was conducted independently by a high school student as part of a research initiative.