Improved Upper Bound on Brun's Constant Under GRH
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910946772910080 |
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| author | Dunn, Lachlan |
| author_facet | Dunn, Lachlan |
| contents | Brun's constant is the summation of the reciprocals of all twin primes, given by $B=\sum_{p \in P_2}{\left( \frac{1}{p} + \frac{1}{p+2}\right)}$. While rigorous unconditional bounds on $B$ are known, we present the first rigorous bound on Brun's constant under the GRH assumption, yielding $B < 2.1594$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15658 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved Upper Bound on Brun's Constant Under GRH Dunn, Lachlan Number Theory 11Y60 (Primary) 11N36 (Secondary) Brun's constant is the summation of the reciprocals of all twin primes, given by $B=\sum_{p \in P_2}{\left( \frac{1}{p} + \frac{1}{p+2}\right)}$. While rigorous unconditional bounds on $B$ are known, we present the first rigorous bound on Brun's constant under the GRH assumption, yielding $B < 2.1594$. |
| title | Improved Upper Bound on Brun's Constant Under GRH |
| topic | Number Theory 11Y60 (Primary) 11N36 (Secondary) |
| url | https://arxiv.org/abs/2504.15658 |