Authors: Stephen Marshall
In number theory, for very difficult Number theory problems that have been open and unsolved for long periods of time it can often be wise to take alternative approaches to the problem. There more old unsolved Number Theory problems than most would think. The Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics, it has been unsolved for over 281 years. On 7 June 1742, the German mathematician Christian Goldbach wrote a letter to Leonhard Euler (letter XLIII) in which he proposed the following conjecture:Every even integer which is ≥ 4 can be written as the sum of two primes. It also states that every even natural number greater than 2 is the sum of two prime numbers. Or more specifically, that the "strong" Goldbach Conjecture asserts that all positive even integers ≥ 4 can be expressed as the sum of two primes. Two primes (p,q) such that p + q = 2n for n a positive integer ≥ 2.The conjecture has been shown via computer to hold for all integers less than 4×1018, but remains unproven despite enormous effort by many mathematicians over hundreds of years. Even the author has spent much effort attempting to solve this conjecture using several different direct methods and have come very close but was not able to prove the Goldbach Conjecture using any of these direct approaches. All of this effort made the author realize how difficult the Goldbach Conjecture is to solve using direct approaches, so this made him consider looking for a back door approach, or a work around the direct approaches. Any such approach could be different than the Goldbach Conjecture, but if it is a different Conjecture must be the equivalent of the Goldbach Conjecture, conjecture otherwise it would not solve the Goldbach Conjecture. This is exactly what the author has done, an equivalent conjecture has been developed and proven, thus solving the Goldbach Conjecture. Therefore, we call this a "back door" proof of the Goldbach Conjecture.
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[v1] 2023-06-14 19:43:27
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