Computation of the least primitive root
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912114447220736 |
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| author | McGown, Kevin J. Sorenson, Jonathan P. |
| author_facet | McGown, Kevin J. Sorenson, Jonathan P. |
| contents | Let $g(p)$ denote the least primitive root modulo $p$, and $h(p)$ the least primitive root modulo $p^2$. We computed $g(p)$ and $h(p)$ for all primes $p\le 10^{16}$. Here we present the results of that computation and prove three theorems as a consequence. In particular, we show that $g(p)<p^{5/8}$ for all primes $p>3$ and that $h(p)<p^{2/3}$ for all primes $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_14193 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Computation of the least primitive root McGown, Kevin J. Sorenson, Jonathan P. Number Theory 11A07, 11Y16 Let $g(p)$ denote the least primitive root modulo $p$, and $h(p)$ the least primitive root modulo $p^2$. We computed $g(p)$ and $h(p)$ for all primes $p\le 10^{16}$. Here we present the results of that computation and prove three theorems as a consequence. In particular, we show that $g(p)<p^{5/8}$ for all primes $p>3$ and that $h(p)<p^{2/3}$ for all primes $p$. |
| title | Computation of the least primitive root |
| topic | Number Theory 11A07, 11Y16 |
| url | https://arxiv.org/abs/2206.14193 |