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If Goldbach's Conjecture holds beyond and including an even number $e$, but this is only proved to be independenteventually true, is it necessarily true for $e$?

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Carlo Beenakker
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Delete this question. Delete If Goldbach's Conjecture holds beyond and including an even number $e$, but this questionis only proved to be independent, is it true for $e$?

Delete this question. Delete this question. Delete this questionWe have all heard that if Goldbach's conjecture is independent, then it is true. Delete this question This is because if GC is false then there is an even number which is not the sum of two primes, and hence a finite proof. Delete What if this questionnumber is very large? Maybe beyond our reach?

If one proves that it is independent that eventually every even number is the sum of two primes, can we conclude that eventually every even number is the sum of two primes? Even if we may never know the $e$ from which it is Goldbach's conjecture, all the way, into infinity?

If we know that there is an $e$ from which every even number after and including $e$ is the sum of two primes, is independent, can we conclude that $e$ and every even number beyond, is the sum of two primes?

Even if we may never know what $e$ is?

Let $e$ be the least even integer such that $e$ is the sum of two primes and for every $k=2n$ where $n \in \mathbb{N}$ where $k$ is greater than $e$, then $k$ is also the sum of two primes. Delete this question Suppose it is independent of ZFC that $e$ exists. Does it follow that $e$ exists?

Delete this question. Delete this question

Delete this question. Delete this question. Delete this question. Delete this question. Delete this question. Delete this question.

If Goldbach's Conjecture holds beyond and including an even number $e$, but this is only proved to be independent, is it true for $e$?

We have all heard that if Goldbach's conjecture is independent, then it is true. This is because if GC is false then there is an even number which is not the sum of two primes, and hence a finite proof. What if this number is very large? Maybe beyond our reach?

If one proves that it is independent that eventually every even number is the sum of two primes, can we conclude that eventually every even number is the sum of two primes? Even if we may never know the $e$ from which it is Goldbach's conjecture, all the way, into infinity?

If we know that there is an $e$ from which every even number after and including $e$ is the sum of two primes, is independent, can we conclude that $e$ and every even number beyond, is the sum of two primes?

Even if we may never know what $e$ is?

Let $e$ be the least even integer such that $e$ is the sum of two primes and for every $k=2n$ where $n \in \mathbb{N}$ where $k$ is greater than $e$, then $k$ is also the sum of two primes. Suppose it is independent of ZFC that $e$ exists. Does it follow that $e$ exists?

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If Goldbach's Conjecture holds beyond and including an even number $e$, but Delete this is only proved to be independent, is it true for $e$?question. Delete this question

We have all heard that if Goldbach's conjecture is independent, then it is trueDelete this question. This is because if GC is false then there is an even number which is not the sum of two primes, and hence a finite proof Delete this question. What if Delete this number is very large? Maybe beyond our reach?

If one proves that it is independent that eventually every even number is the sum of two primes, can we conclude that eventually every even number is the sum of two primes? Even if we may never know the $e$ from which it is Goldbach's conjecture, all the way, into infinity?

If we know that there is an $e$ from which every even number after and including $e$ is the sum of two primes, is independent, can we conclude that $e$ and every even number beyond, is the sum of two primes?

Even if we may never know what $e$ is?

Let $e$ be the least even integer such that $e$ is the sum of two primes and for every $k=2n$ where $n \in \mathbb{N}$ where $k$ is greater than $e$, then $k$ is also the sum of two primesquestion. Suppose it is independent of ZFC that $e$ exists Delete this question. Does it follow that $e$ exists? Delete this question. Delete this question.

If Goldbach's Conjecture holds beyond and including an even number $e$, but this is only proved to be independent, is it true for $e$?

We have all heard that if Goldbach's conjecture is independent, then it is true. This is because if GC is false then there is an even number which is not the sum of two primes, and hence a finite proof. What if this number is very large? Maybe beyond our reach?

If one proves that it is independent that eventually every even number is the sum of two primes, can we conclude that eventually every even number is the sum of two primes? Even if we may never know the $e$ from which it is Goldbach's conjecture, all the way, into infinity?

If we know that there is an $e$ from which every even number after and including $e$ is the sum of two primes, is independent, can we conclude that $e$ and every even number beyond, is the sum of two primes?

Even if we may never know what $e$ is?

Let $e$ be the least even integer such that $e$ is the sum of two primes and for every $k=2n$ where $n \in \mathbb{N}$ where $k$ is greater than $e$, then $k$ is also the sum of two primes. Suppose it is independent of ZFC that $e$ exists. Does it follow that $e$ exists?

Delete this question. Delete this question

Delete this question. Delete this question. Delete this question. Delete this question. Delete this question. Delete this question.

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Andrés E. Caicedo
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