# 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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### 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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### Why doesn't proof of the weak Goldbach conjecture also prove the strong Goldbach conjecture?

The weak Goldbach conjecture can take the representation O = a + b + c, where O is an odd number greater than 5, and a, b, c are prime. It can thus also take the form O - a = b + c. Since at least one ...
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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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### Equivalence between Goldbach and Euler's statements

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 ... 86 views

### 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 ...
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### Is it possible to prove certain conjectures have no proof?

We will use Goldbach's conjecture as an example$^1$. It is either true or false that every even number greater than 2 is the sum of two primes. Let's take a look at these two scenarios. Goldbach's ...
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### Approach towards proving some symmetries of prime numbers

Reviewing draft documents from years ago, I found an interesting line of reasoning for approaching a proof of what I called the "symmetry conjecture" about prime numbers, which can be stated ...
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