The 2 Goldbach's Conjectures with Proof

Published: 11 February 2021| Version 1 | DOI: 10.17632/6nnfmth838.1
nikos mantzakouras


The 1741 Goldbach [1] made his most famous contribution to mathematics with the conjecture that all even numbers can be expressed as the sum of the two primes (currently Conjecture referred to as "all even numbers greater than 2 can be expressed as the sum-two primes) .Yet, no proof of Goldbach's Conjecture has been found. This assumption seems to be right for a large amount of numbers using numerical calculations. Some examples are 10 = 3 + 7, 18 = 7 + 11, 100 = 97 + 3, and so on. But there are a multitude sums primes meeting an even number which I would say is irregular, but increases with the size of the even number.To same happens and with an odd number as example 25, ie. 25 = 3 + 3 + 19 = 3 + 5 + 17 = 3 + 11 + 11 = 5 + 7 + 13 = 7 + 7 + 11. We say only 5 cases and only those that meet the constant sum of 25 .First turns in Theorem 3 that there may be at least a pair of primes, such that their sum is equal to every even number. But at the same time reveals the method of finding all pairs that satisfy this condition. According to Theorem 4, the second guess switches to form first guess and this is primarily elementary, to prove the truth of 1.The alternative and the side stream assistant, to prove Goldbach's Conjecture in this research was the Mathematica program which is the main tool for data collection, but also for finding all the steps in order to demonstrate each part of the proof. We must mention that Vinogradov proved to1937, that for every sufficiently large number can be expressed, that is the sum of the three primes. And finally the Chinese mathematician Chen Jing Run proved big first for a constant number that is the sum of the first three in 1966 [2]. Finally, the investigation of Goldbach's Conjecture has acted as a catalyst for the creation and development of many methods that are useful, with many theorems that help and other areas of mathematics.



Number Theory, Approximation Theory, Algebra of Analytic Functions, Elementary Theory of Primes