Density ternary Goldbach for primes in a fixed residue class

Q: What type of study is this?

This is a Quantitative Study study.

Ali Alsetri

doi:10.48550/arxiv.2505.09648

May 13, 2025Open Access

Density ternary Goldbach for primes in a fixed residue class

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Key Points

Every sufficiently large odd integer can be expressed as a sum of three primes from a dense subset.
If the relative density of primes is above 50%, it ensures representability for certain integers.
The threshold for relative density is shown to be optimal in this context, confirming previous conjectures.
This work builds on Goldbach's conjecture in a specific prime residue class, providing new insights.

Implication

The proof demonstrates that a dense subset of primes can sum to specific integers, highlighting threshold significance.

Abstract

We prove that if A is a subset of those primes which are congruent to 1 3 such that the relative density of A in this residue class is larger than 1/2, then every sufficiently large odd integer n which satisfies n ≡ 0 3 can be written as a sum of three primes from $A.$ Moreover the threshold of 1/2 for the relative density is best possible.

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Cite This Study

Ali Alsetri (2025) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac361c0 https://doi.org/10.48550/arxiv.2505.09648

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Density ternary Goldbach for primes in a fixed residue class

Key Points

Implication

Abstract

Discussion

Cite This Study

Density ternary Goldbach for primes in a fixed residue class

Key Points

Implication

Abstract

Discussion

Cite This Study

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