International Journal of Media and Networks(IJMN)
ISSN: 2995-3286 | DOI: 10.33140/IJMN
Impact Factor: 1.02
Short Article - (2025) Volume 3, Issue 5
An Elementary Proof of the Goldbach Conjecture for n ≥ 8
Received Date: Aug 01, 2025 / Accepted Date: Aug 29, 2025 / Published Date: Sep 07, 2025
Copyright: ©2025 Oscar Melchor, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation: Garcia, G., Melchor, O. (2025). An Elementary Proof of the Goldbach Conjecture for n?8. Int J Med Net, 3(5), 01-02.
Abstract
An elementary proof of the strong form of the Goldbach Conjecture is presented: every even number greater than 2 can be expressed as the sum of two prime num- bers. The strategy is based on analyzing the possible pairs of odd numbers that sum up to 2n and applying a sieve based on the divisibility of primes less than or equal to √ 2n. It is shown that for n ≥ 8, at least one of these pairs consists of two prime numbers.
Introduction
The Goldbach Conjecture states that every even number greater than two can be written as the sum of two prime numbers. Despite extensive computational verification up to a very large limits a general accepted proof has yet to be established.In this paper,we present an elimentary approach that establishes the conjecture for all n € N such that n >8
construction of the pairs
Elimination Criterion
Validity of the sieve
Number of the Surviving Pairs
Conclusion
