A weak method to come close to solution of Goldbach conjecture

Abstract

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 conjecture follows from the result, where Ln is the largest strong Goldbach number generated by the n-th prime Pn and denotes an even number such that every even number from 4 to Ln is the sum of two primes among the first n primes but Ln + 2 is not such a sum. It means Pn − n log n is the smallest possible value of Ln for n ≥ 1 to support Goldbach conjecture, therefore, Goldbach conjecture is true if it can be proven that Ln > Pn − n log n for n ≥ 1. Mathematics Subject Classification: 11A41