On Maximal Prime Gaps
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914588850651136 |
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| author | Wang, Cheng-TIng |
| author_facet | Wang, Cheng-TIng |
| contents | In this paper, we show a new upper bound of prime gaps, that is the gap between a prime number and its consecutive prime number. We show that the gap between a prime number $p_n$ and its consecutive prime number is not larger than $2\log^2{p_n}$. We also show that the result implies the existence of a prime number in a certain type of interval for large enough numbers as a consequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Maximal Prime Gaps Wang, Cheng-TIng Number Theory 11A41, 11N05 In this paper, we show a new upper bound of prime gaps, that is the gap between a prime number and its consecutive prime number. We show that the gap between a prime number $p_n$ and its consecutive prime number is not larger than $2\log^2{p_n}$. We also show that the result implies the existence of a prime number in a certain type of interval for large enough numbers as a consequence. |
| title | On Maximal Prime Gaps |
| topic | Number Theory 11A41, 11N05 |
| url | https://arxiv.org/abs/2605.14871 |