# Questions tagged [goldbachs-conjecture]

For questions about Goldbach's conjecture: every even integer greater than two is the sum of two primes.

57 questions
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### Goldbach for certain classes of $n$

The Wiki article on the Goldbach conjecture (where $\#$ of ways even $n$ can be represented by prime additions is heareafter denoted $G(n)$) states that In 1975, Hugh Montgomery and Robert Charles ...
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### Implications of disproving the Goldbach's Conjecture

What would be the most important implications of finding an even number that cannot be expressed as the sum of two primes? Would the existence on one such number in anyway predict the likeliness of ...
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### Is every integer $\geq5$ the sum of two primes and a power of a prime?

Is every integer $\geq5$ the sum of two primes and a power of a prime (where $1$ is included in the prime powers)? I don't really expect someone to prove this here, but I wonder if the question has ...
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### What are the missing gaps to prove Goldbach Conjecture?

When Andrew Wiles proved FLT, all he needed to do was to prove "semi-stable elliptic curve case" of Shimura-Taniyama conjecture. He did not need to start from scratch, he just needed to fill this ...
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### Best upper bound for $r_{0}(n)$ under Goldbach and Chowla's conjectures

Assume Goldbach's conjecture. Then for any large enough composite integer $n$ $r_{0}(n) : =\inf\{r\ge 0,(n-r,n+r)\in\mathbb{P}^{2}\}$ exists and is obviously smaller than $n$ . Does the ...
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### Related to proving Goldbach's Conjecture

How significant would it be to prove that every even number larger than $49$ can be written as the sum of two integers co-prime to $2, 3, 5,$ and $7$? I came across this result incidentally when ...
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### A Generalization of Goldbach’s Conjecture

The Goldbach's conjecture is that $\forall n \in \mathbb{N}^*, \ \exists p,q \in \mathcal{P}$ such that $2n=p+q$. I wonder if there are some generalization giving more information about the ...
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### Does Linnik's approximation to Goldbach's problem also work for the power of 3, 5, 7, etc ?

Linnik proved in 1951 the existence of a constant K such that every sufficiently large even number is the sum of two primes and at most K powers of 2. Roger Heath-Brown and Jan-Christoph Schlage-...
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### Equivalent conjecture to Goldbach's conjecture

I'm reading a paper regrading the basis orders. In that paper, I met with the following statement: $$3(\mathbb{P}\cup\{0 \})=\mathbb{Z}_{\geq 2}$$, Which, by definition, states that primes form ...