On the Maximal Gap between Primes
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917057712357376 |
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| author | Wang, Cheng-Ting |
| author_facet | Wang, Cheng-Ting |
| contents | In this paper, we show some results about the gap between a prime number and its consecutive prime number for large enough prime numbers. 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_2510_17065 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Maximal Gap between Primes Wang, Cheng-Ting General Mathematics 11A41, 11N05 In this paper, we show some results about the gap between a prime number and its consecutive prime number for large enough prime numbers. 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 the Maximal Gap between Primes |
| topic | General Mathematics 11A41, 11N05 |
| url | https://arxiv.org/abs/2510.17065 |