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# Numerical verification of the Goldbach conjecture

ABSTRACT: The Strong Goldbach conjecture, GC, dates back to $1742$. It states that every even integer greater than four can be written as the sum of two prime numbers. Since then, no one has been able to prove the conjecture. The conjecture has been verified to be true for all even integers up to $4.10^{{18}}$. In this article, we prove that the conjecture is true for all integers, with at least three different ways. In short, this treaty has as objective show the proof of GC, and presents a new resolution to the conjecture. Knowing that, these infinities establish other groups of infinities, in a logical way the conviction for the method and idea of proving it, we stand and separate these groups to prove, not only a sequence, but the whole embodiment of arithmetic

^{}properties called here as groups, as well as its infinity conjectured for centuries.

Keywords: Goldbach’s Conjecture; Crystallographic group; Cobordism group; Algebraic number theory; Multiprime Theorem’s; Productoria Table.

AMS Subject Classification: 11N05; 11A41; 11A25; 11Y11; 11P32; 05A10; 11N56; 11D99; 11P99; 11N32; 05A17.

## Mathematics Subject Classification

11N05*no label found*11A41

*no label found*11A25

*no label found*11Y11

*no label found*11P32

*no label found*05A10

*no label found*11N56

*no label found*11D99

*no label found*11P99

*no label found*11N32

*no label found*05A17

*no label found*

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The pdf is missing on the tab, can you please reattach it?

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