# 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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### Explain this method for generating Mersenne Primes based on Lagrange interpolation

This question is about the work A Method for Generating Mersenne Primes and the Extent of the Sequence of the Even Perfect Numbers. In the 3rd section you will read: I don't understand understand ...
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### The Goldbach Conjecture | Decomposition to Large Numbers

I find some interesting phenomenon about the Goldbach Conjecture using statistic method, and want to share and discuss with you all. P.S. I have tried to follow the guideline as I can and provide ...
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### Dubious proof of "if Goldbach’s conjecture is unprovable, it must be true"

Recently, I read a news article written by an "emeritus professor at UCD school of mathematics and statistics" that made the following curious claim about the Goldbach's conjecture: "...
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### Is it possible to have this overlap between Goldbach and the twin prime conjectures?

This question is related to this. But, here it is related Goldbach's conjecture. Any even number greater than $4$ is the result of addition of two prime numbers one of which is the lower of a twin ...
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### Every even number is the sum of at most three primes

I'm failing to find online references to the following problem, which to me seems a slight weakening of the Goldbach conjecture. Conjecture: every even integer $n$ is the sum of at most three primes. ...
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### Number of even integers not satisfying Goldbach's conjecture from Vinogradov. Infinity of numbers not satisfying the Goldbach's conjecture.

If $A(x)$ is the number of even integers less than $x$ that don't write as a sum of two (odd) primes, then $$\lim_{x\to \infty} \frac{A(x)}{x} = 0$$ That is what is written in my book (Elementary ...
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### Can we use the proof of the weak Goldbach conjecture to also prove the strong Goldbach conjecture?

Why doesn't proof of the weak Goldbach conjecture also prove the strong Goldbach conjecture? Actually I am referring to this link. My question is why the logic used in this question cannot be used ...
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### 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 ...
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### Is the sequence $p_n-n+1$ related to the Goldbach conjecture via the Dirichlet inverse of of the Euler totient?

I am trying to learn what the Goldbach conjecture is and I therefore ran this Mathematica program where I tried to incorporate the conjecture: ...
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### Is it true that for sequences that satisfy the property-type in Goldbach's conjecture, there is an integer which cannot be expressed in a unique way?

Let $A\subset \mathbb{Z}$ be such that $\exists\ c\in\mathbb{Z}$ such that $\forall\ n\geq c: \exists\ a,a'\in A$ with $a+a' = n.$ In other words, $A$ satisfies sort-of Goldbach conjecture, but for ...
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### Odd semiprimes as differences of two even perfect squares, divided by 4 - consequences regarding Goldbach's Conjecture?

My observation is that every odd semiprime can be written as the difference of two even perfect squares, divided by 4, or, in other words, in order to locate--and possibly factorize--odd semiprimes, ...
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### Does Goldbach's Conjecture hold true for other conditions?

I have been reading up on Goldbach's conjecture and how I understand it is as follows: For all values of x that satisfy x % 2 == 0, where x is an element from the set of natural numbers starting at 4, ...
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### Properties of the even number that doesn't satisfy the Golbach's Conjecture. [closed]

This is a little vague question, but I think this is the best place to ask it. We haven't found an even number which cannot be written as a sum of two primes, but mathematicians must have studied that ...
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### Is it possible that every $P$ as a prime number, can be expressed as a prime factor of $E$ such that $E$ is the sum of a pair of twin primes?

Curious about the Goldbach conjecture, and reading about twin primes, I was wondering if it is possible that every prime number as $P$, can be expressed as a prime factor of at least one $E$ such that ...
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We know that Goldbach wrote Euler, saying every integer greater than or equal to $6$ is the sum of three prime numbers. Euler responded by saying an equivalent statement is that even integers greater ...
### Assuming the Goldbach conjectures are true, will all $O$ and $O ⋅ 2$ share at least $1$ of the $p$'s in such a way that the remaining are also $p$'s?
Assuming the Even Goldbach conjecture is true, it will mean that every even number greater than $2$ as $E$ can be represented as the sum of $2$ primes as $p$'s Assuming the Odd Goldbach conjecture is ...