New Computing Model of $GN_eTM$ Turing Machine On Solving Even Goldbach Conjecture

TL;DR

This paper introduces a new computational model called $GN_eTM$ Turing Machine to explore the even Goldbach conjecture, providing theoretical proofs of its infinite existence and related criteria.

Contribution

The paper presents a novel $GN_eTM$ model, establishes criteria for the conjecture's probability, and proves the infinite existence of solutions without halting problem limitations.

Findings

Proves the infinite existence of solutions to the even Goldbach conjecture.

Develops a new $GN_eTM$ model for conjecture verification.

Shows the conjecture's solutions are not limited by halting problem constraints.

Abstract

Based on the propositional description of even Goldbach conjecture, in order to verify the truth of even Goldbach conjecture, we will deeply discuss this question and present a new computing model of $G{{N}_{e}}TM$ Turing Machine. This paper proves the infinite existence of even Goldbach's conjecture and obtains the following new results: 1. The criterion of general probability speculation of the existence judgment for even Goldbach conjecture is studied, and which at least have a formula satisfy the deduction result of matching requirements for even Goldbach conjecture in the model $\bmod \overset{\equiv }{\mathop{M}}\,({{N}_{e}})$. 2. In the controller of the $G{{N}_{e}}TM$ model, the algorithm problem of the prime matching rule is given, regardless of whether the computer can be recursively solved, the rule algorithm for designing prime numbers in controllers is computer recursively solvable. 3. The judgment problem that about even Goldbach conjecture whether infinite existence is studied. The new research result has shown that according to the constitution model of the full arranged matrix of given even number ${N}_{e}$, and if only given an even number ${N}_{e}$, it certainly exists the matrix model $Mod\overset{\equiv }{\mathop{X}}\,(p)$ and is proved to be equivalent. Therefore, it proves indirectly that the model $G{{N}_{e}}TM$ does not exist halting problem, and it also indicate that the even Goldbach conjecture is infinity existence.