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# Questions tagged [goldbachs-conjecture]

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

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95 votes
3 answers
9k views

### Decidability of the Riemann Hypothesis vs. the Goldbach Conjecture

In the most recent numberphile video, Marcus du Sautoy claims that a proof for the Riemann hypothesis must exist (starts at the 12 minute mark). His reasoning goes as follows: If the hypothesis is ...
• 2,268
26 votes
1 answer
4k views

### Could it be that Goldbach conjecture is undecidable?

The result closest to Goldbach conjecture is Chen's theorem [Sci. Sinica 16 157–176], the proposition 1+2''. It is natural to ask if it is likely that under our arithmetic axioms the Goldbach ...
• 20.8k
6 votes
0 answers
322 views

### Does the set of $m \in Max(ord_n(k))$ for every $n$ without primitive roots contain a pair of primes $p_1+p_2=n$?

I have made the following observation: for those n even numbers that do not have primitive roots modulo n ,$Pr(n)$, the set $M(n)$ of those $k$ having a maximum multiplicative order $ord_n(k)$ ...
• 8,923
17 votes
9 answers
1k views

### What are some equivalent statements of (strong) Goldbach Conjecture?

What are some equivalent statements of (strong) Goldbach Conjecture ? We all know that Riemann Hypothesis has some interesting equivalent statements. My favorites are involved with Mertens ...
• 279
5 votes
1 answer
934 views

### The relationship between Golbach's Conjecture and the Riemann Hypothesis

My question pertains to two famous groups of related conjectures: Goldbach's Conjecture (GC); Goldbach's Weak Conjecture (GWC); The Riemann Hypothesis (RH); The Generalized Riemann Hypothesis (GRH). ...
• 306
4 votes
1 answer
356 views

• 6,044
3 votes
0 answers
365 views

### Is every positive integer greater than $2$ the sum of a prime and two squares?

I'm not sure if this conjecture is less hard than Goldbachs conjecture: any integer greater than $2$ is the sum of an odd prime and two squares of integers. Facts as: Every prime of the form $4n+1$ ...
• 13.9k
3 votes
0 answers
228 views

### Is the weak Goldbach conjecture proved? [duplicate]

The Wikipedia page of the Goldbach's weak conjecture states that "In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. As of 2018, the proof is widely accepted in the ...
• 157
3 votes
0 answers
329 views

### What is the relationship between GRH and Goldbach Conjecture?

We know that we can prove weak Goldbach Conjecture (three prime theorem) if we assume GRH (Hardy-Littlewood had proved this). Can we also prove strong Goldbach Conjecture if we assume GRH ? Also, ...
• 31
3 votes
2 answers
663 views

### Any results for small number Goldbach conjecture research?

It seems to me that most research results on Goldbach conjecture research are for large number. (Example: results of Vinogradov, Terence Tao, Harald Helfgott, etc). My understanding is that those ...
• 31
2 votes
2 answers
95 views

### Reaching higher even numbers in Goldbach's conjecture, using lower even numbers.

Let $n \in \Bbb{N}, n \gt 1$. Let $\Bbb{P} =$ the prime numbers in $\Bbb{N}$. Define \begin{align*} A_n &= \{ (p,q) \in \Bbb{P}^2 : p + q = 2n\}, \\ B_n &= \{ (p, q) : p - q = 2n \}. \end{...
• 21.8k
2 votes
1 answer
454 views

### Goldbach conjecture: Every integer $n>3$ is halfway between $2$ primes.

Prove that the following conjecture is equivalent to the strong Goldbach conjecture: Every integer $n>3$ is halfway between $2$ primes. I'm able to prove it, but i don't have much experience in ...
• 1,282
1 vote
0 answers
192 views

• 672