International Journal of Mathematics and Statistics Studies (IJMSS)

EA Journals

Goldbach’s Conjecture

A Full and Detailed Proof for the Riemann Hypothesis & the Simple Inductive proof of Goldbach’s Conjecture (Published)

As in my previous two papers [2] & [3] about the boundary of the prime gap still cause some misunderstanding, I here in this paper tries to clarify those detailed steps in proving such boundary of the prime gap for a contradiction. Indeed, the general idea of my designed proof is to make all of the feasible case of the Riemann Zeta function with exponents ranged from 1 to s = u + v*I becomes nonsense (where u, v are real numbers with I is imaginary equals to (-1)1/2 except that u = 0.5 with some real numbers v as the expected zeta roots. Once if we can exclude all other possibilies unless u = 0.5 with some real numbers v in the Riemann Zeta function’s exponent “s”, then the Riemann Hypothesis will be proved immediately. The truth of the hypothesis further implies that there is a need for the shift from the line x = 0 to the line x = 0.5 as all of the zeta roots lie on it. However, NOT all of the points on x = 0.5 are zeros as we may find from the model equation that has been well established in [2]. One of my application is in the quantum filtering for an elimination of noise in a quantum system but NOT used to filter human beings like the political counter-parts.In general, this author suggests that for all of the proof or disproof to any cases of hypothesis, one may need to point out those logical contradictions [14] among them. Actually, my proposition works very well for the cases in my disproof of Continuum Hypothesis [15] together with the proof in Riemann Hypothesis etc.

Keywords: Goldbach’s Conjecture, Riemann hypothesis, detailed proof, simple inductive proof


In this paper, an attempt was made to present a review on Goldbach’s conjecture as well as a remarkable result derived from it. In fact, according to Goldbach’s conjecture, it can be concluded that if n is a natural number, there is at least one prime number between n and 2n, in a way that n<p<2n. In other words, it is claimed that Bertrand postulate is included in Goldbach’s conjecture. Moreover, another characteristic of prime numbers will be presented which states that for each prime number, P, there are two other prime numbers such as Pa and Pb in a way that P is equidistant from Pa and Pb. Therefore, the present article claims that Bertrand Postulate is hidden within Goldbach’s conjecture

Keywords: Bertrand Postulate, Goldbach’s Conjecture, Prime Numbers

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