  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.
