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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.14369 |
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| _version_ | 1866914565421268992 |
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| author | Hu, Xiaoyang Gao, Meng |
| author_facet | Hu, Xiaoyang Gao, Meng |
| contents | Let $\mathcal{P}$ denote the set of all primes, and let $\underlineδ(P)$ denote the relative lower density of a subset $P$ in $\mathcal{P}$. Suppose that $P_1, P_2, P_3, P_4$ are four subsets of primes with $\underlineδ(P_1)+\underlineδ(P_2)>1$ and $ \underlineδ(P_3)+\underlineδ(P_4)>1.$ Then for every sufficiently large even integer $n$, there exist primes $p_i \in P_i$ $(i=1,2,3,4)$ such that $n=p_1+p_2+p_3+p_4$. The condition is the best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A density version of quaternary Goldbach problem Hu, Xiaoyang Gao, Meng Number Theory Let $\mathcal{P}$ denote the set of all primes, and let $\underlineδ(P)$ denote the relative lower density of a subset $P$ in $\mathcal{P}$. Suppose that $P_1, P_2, P_3, P_4$ are four subsets of primes with $\underlineδ(P_1)+\underlineδ(P_2)>1$ and $ \underlineδ(P_3)+\underlineδ(P_4)>1.$ Then for every sufficiently large even integer $n$, there exist primes $p_i \in P_i$ $(i=1,2,3,4)$ such that $n=p_1+p_2+p_3+p_4$. The condition is the best possible. |
| title | A density version of quaternary Goldbach problem |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.14369 |