# Questions tagged [goldbachs-conjecture]

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

141 questions
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### Is there any algorithm to identify the smallest example of gap size $n-1$ between consecutive prime numbers

In contemplating Goldbach's conjecture, I became interested in gaps between successive primes. If $n<a<b<2n$ and the range $a$ to $b$ is a primeless gap, then one could ignore any primes in ...
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### Every integer greater than $0$ can be expressed as a sum of $a$'s and $b$'s, if and only if $a$ and $b$ have no common factor

Every integer greater than $0$ can be expressed as a sum of $a$'s and $b$'s, if and only if $a$ and $b$ have no common factor. PROOF: Consider the case $a=5$, $b=13$. First, let's find how to ...
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### Goldbach Conjecture, a simple statement. [closed]

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 ...
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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 ...
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### $O(1)$ algorithm for Goldbach partitions, assuming $\pi(n)$ is known for all $0<n<2n$?

Instead of a list of prime numbers, we will be using $B_{p}(2n)$, a binary representation of the distribution of prime numbers from $3$ to $2n$. Simply writing 0 for non-primes and 1 for primes, we ...
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### Is there any known relationship between Goldbach's comet G(n) and the prime counting function (${\pi(n)}$)?

The "extended" Goldbach conjecture defines R(n) as the number of representations of an even number n as the sum of two primes, but the approach is not related directly with ${\pi(n)}$, is there any ...
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### Upper bound for the number of representation numbers as the sum of two primes

To prove strong goldbach conjecture one can use a lower bound of number of the representations of a number as the sum of two primes. If its greater than zero, than we have conjecture. I wonder if ...
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### Lower bound for $g(n)$, the number of decompositions of 2n into ordered sums of two odd primes

I was coding an algorithm that calculates $g(n)$, the number of decomposition of 2n into ordered sums of two odd primes (A002372), or the number of Goldbach partitions. I noticed i can express the ...
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### Goldbach's Conjecture and 1-1 correspondence [closed]

I know math only (somewhat) as a recreation, so I know this is a naive and ignorant question, but I don't have the mathematical terminology or experience to figure out why it has to be incorrect. I am ...