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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.

The Goldbach conjecture originates from a $1742$ letter from Goldbach to Euler, states that every even integer greater than $3$ is the sum of two primes. The conjecture has been shown to hold for all integers less than $4 × 10^{18}$, but remains unproven despite considerable effort.

Goldbach's weak conjecture is that every odd integer greater than $6$ is the sum of three primes.

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Are there any large numbers found that seemed eerily close to disproving Goldbach's conjecture?

This question is about any numbers that seemed unusually close to disproving Goldbach's conjecture. Meaning any large numbers (say above 100) that had very few sets of primes which satisfied the conjecture. I imagine the number of sets increases…
Juel Herbranson
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Has Goldbach's Conjecture been proven?

When I searched for the proofs for Goldbach's Conjecture, there seems to be a handful (or more) of papers that attempt to solve it. Are there any official proofs out there yet?
Binh Ho
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Even numbers sum of two primes

We don't know if the Goldbach conjecture is true, but do we we know some type of even numbers which can be expressed as sum of two prime numbers (excluding the trivial sums of two prime numbers) ? Edit : I am searching an infinite set $S$ of even…
PainBouchon
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Why can't we prove Goldbach's conjecture with this method?

1: Prime gap bounds: Consider the following non-asymptotic bounds for $\pi(x)$, proven by Dusart in 2018 (holding for $x>5393$): $$\frac{x}{\log(x)-1}<\pi(x)<\frac{x}{\log(x)-1.112}$$ To get the maximum value for $p(n)$, we take the lower bound with…
François Huppé
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Should Goldbach's Conjecture be restated thus? *Every integer $>3$ can be expressed as the average of two primes.*

Yes, every, not just even. If a number is the average (or difference) of two primes, by doubling the number it has a partition of those two primes. So, for example, $(7+31)/2=19$ becomes $7+31=2*19=38$. Since every $n*2$ is even, GC has an…
michaelmross
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Goldbach Conjecture Counterexample

My professor introduced the Goldbach Conjecture to me a couple months ago, and I've been intrigued by it ever since. The Goldbach Conjecture states that every even number greater than 4 can be written as the sum of two primes. If we look at the…
Ash
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Goldbach Conjencture - The Binary Pattern

Introduction Hello fellow mathematicians. I am a programmer (uni student) but I've fallen in love with mathematics especially number theory and although I am quite aware of the difficulty on some of those "unsolved problems" and the fact that…
Ilhan
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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, x is the sum of 2 primes numbers I was wondering…
Curious_Student
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Properties of the even number that doesn't satisfy the Golbach's Conjecture.

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 what sort of properties such a number should…
Rounak Sarkar
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Need help with this Goldbach approach.

I have plotted the counts of Goldbach $2n$ sums of primes, below. It is easy to see that the counts of composites gradually decreases relative to $n$ and would like a suggestion on how to prove something like this. We use $n$ as the index to the odd…
Fred Daniel Kline
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Is there the following generalization of Goldbach's weak conjecture?

I heard that the following has been proved: Every odd number greater than 7 can be expressed as the sum of three odd primes. What do we know about the following? There is a $k\in\mathbb N$ such that for every $n\in \mathbb N$, $2n+1>7$ there exists…
curious
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Goldbach conjecture - what's wrong with this "proof"?

Can somebody please tell me what is wrong with the following "proof" of the strong Goldbach Conjecture? For every even number $n$, there are $\frac{n}{4}$ pairs of odd numbers $[a, b]$ such that $a+b=n$ and $a\le b$. If either $a$ or $b$ is not…
tomerius
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The Goldbach Conjecture, its negation and consistency

I am only broadly familiar with mathematics, so please have patience with me. I am wondering about the consistency of both the (a) Goldbach Conjecture and (b) its negation. If the Goldbach Conjecture would be decided, then would we see that (a) or…
Lukas
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Goldbach Conjecture, a simple statement.

I have been trying to figure out(prove) Goldbach Conjecture(Strong) which states: Every even integer greater than 2 can be expressed as the sum of two primes. My question I guess is general, is it wrong for me to prove something using "simple…
Alaa
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