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A heuristic study of the distribution of primes in short and not-so-short intervals
A numerical study on the distributions of primes in short intervals of length $h$ over the natural numbers $N$ is presented. Based on Cram\'er's model in Number Theory, we obtain a heuristic expression applicable when $h \gg \log{N}$ but $h \ll N$, providing support to the Montgomery and S...
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| Lenguaje: | eng |
| Publicado: |
2018
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| Acceso en línea: | http://cds.cern.ch/record/2649937 |
| _version_ | 1780960776565030912 |
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| author | Sanchis-Lozano, Miguel-Angel |
| author_facet | Sanchis-Lozano, Miguel-Angel |
| author_sort | Sanchis-Lozano, Miguel-Angel |
| collection | CERN |
| description | A numerical study on the distributions of primes in short intervals of length
$h$ over the natural numbers $N$ is presented. Based on Cram\'er's model in
Number Theory, we obtain a heuristic expression applicable when $h \gg \log{N}$
but $h \ll N$, providing support to the Montgomery and Soundararajan conjecture
on the variance of the prime distribution at this scale. |
| id | cern-2649937 |
| institution | Organización Europea para la Investigación Nuclear |
| language | eng |
| publishDate | 2018 |
| record_format | invenio |
| spelling | cern-26499372021-09-17T12:50:10Zhttp://cds.cern.ch/record/2649937engSanchis-Lozano, Miguel-AngelA heuristic study of the distribution of primes in short and not-so-short intervalsmath.NTMathematical Physics and MathematicsA numerical study on the distributions of primes in short intervals of length $h$ over the natural numbers $N$ is presented. Based on Cram\'er's model in Number Theory, we obtain a heuristic expression applicable when $h \gg \log{N}$ but $h \ll N$, providing support to the Montgomery and Soundararajan conjecture on the variance of the prime distribution at this scale.arXiv:1804.07659CERN-TH-2018-83oai:cds.cern.ch:26499372018 |
| spellingShingle | math.NT Mathematical Physics and Mathematics Sanchis-Lozano, Miguel-Angel A heuristic study of the distribution of primes in short and not-so-short intervals |
| title | A heuristic study of the distribution of primes in short and not-so-short intervals |
| title_full | A heuristic study of the distribution of primes in short and not-so-short intervals |
| title_fullStr | A heuristic study of the distribution of primes in short and not-so-short intervals |
| title_full_unstemmed | A heuristic study of the distribution of primes in short and not-so-short intervals |
| title_short | A heuristic study of the distribution of primes in short and not-so-short intervals |
| title_sort | heuristic study of the distribution of primes in short and not-so-short intervals |
| topic | math.NT Mathematical Physics and Mathematics |
| url | http://cds.cern.ch/record/2649937 |
| work_keys_str_mv | AT sanchislozanomiguelangel aheuristicstudyofthedistributionofprimesinshortandnotsoshortintervals AT sanchislozanomiguelangel heuristicstudyofthedistributionofprimesinshortandnotsoshortintervals |