Number Theory

    

An Elementary Proof of the Goldbach Conjecture for N ≥ 8

Authors: Gustavo García, Oscar Melchor

Anelementary 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 numbers. 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.

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[v1] 2025-08-06 20:42:13

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