A weak method to come close to solution of Goldbach conjecture

摘要

In this note we proved that if Ln ≥ Pn ? n log n for n ≥ 1 then Ln → ∞ as n → ∞using the prime number theorem and Rosser theorem, and Goldbach conjecturefollows from the result, where Ln is the largest strong Goldbach number generatedby the n-th prime Pn and denotes an even number such that every even numberfrom 4 to Ln is the sum of two primes among the first n primes but Ln + 2 is notsuch a sum. It means Pn ? n log n is the smallest possible value of Ln for n ≥ 1 tosupport Goldbach conjecture, therefore, Goldbach conjecture is true if it can beproven that Ln Pn ? n log n for n ≥ 1.