On the frequency of small gaps between the primes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909607784349696 |
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| author | Magyar, Akos Pintz, Janos |
| author_facet | Magyar, Akos Pintz, Janos |
| contents | In a recent work Friedlander studied the problem of how large consecutive prime gaps should be in order that the sum of the reciprocals should be divergent. Supposing a very deep Hypothesis, a generalization of the Hardy--Littlewood prime $k$-tuple conjecture, he gave an almost precise answer for it. In the present work we give an unconditional answer for a much weaker form of the same problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the frequency of small gaps between the primes Magyar, Akos Pintz, Janos Number Theory 11N05 (Primary) 11N36 (Secondary) In a recent work Friedlander studied the problem of how large consecutive prime gaps should be in order that the sum of the reciprocals should be divergent. Supposing a very deep Hypothesis, a generalization of the Hardy--Littlewood prime $k$-tuple conjecture, he gave an almost precise answer for it. In the present work we give an unconditional answer for a much weaker form of the same problem. |
| title | On the frequency of small gaps between the primes |
| topic | Number Theory 11N05 (Primary) 11N36 (Secondary) |
| url | https://arxiv.org/abs/2505.07630 |