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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.02769 |
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| _version_ | 1866909932914212864 |
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| author | Akeno, Mizuki |
| author_facet | Akeno, Mizuki |
| contents | We study small gaps between Goldbach primes $\mathbb{P} \cap (N-\mathbb{P})$ using the Bombieri-Davenport method and the Maynard-Tao method, and compare the two.
We show that for almost all even integers $N$, the smallest gap in $\mathbb{P} \cap (N-\mathbb{P})$ is at most $0.765\ldots$ times the average gap, using the Bombieri-Davenport method. This improves a recent result of Tsuda. We also demonstrate that a straightforward application of the Maynard-Tao method is insufficient to improve this bound. However, it allows us to establish the existence of bounded gaps between Goldbach primes with bounded error for almost all even integers $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Small gaps between Goldbach primes Akeno, Mizuki Number Theory We study small gaps between Goldbach primes $\mathbb{P} \cap (N-\mathbb{P})$ using the Bombieri-Davenport method and the Maynard-Tao method, and compare the two. We show that for almost all even integers $N$, the smallest gap in $\mathbb{P} \cap (N-\mathbb{P})$ is at most $0.765\ldots$ times the average gap, using the Bombieri-Davenport method. This improves a recent result of Tsuda. We also demonstrate that a straightforward application of the Maynard-Tao method is insufficient to improve this bound. However, it allows us to establish the existence of bounded gaps between Goldbach primes with bounded error for almost all even integers $N$. |
| title | Small gaps between Goldbach primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.02769 |