Enviar artigo por via de e-mail Prime avoiding numbers is a basis of order 2
- Autores: Gabdullin M.R.1,2, Radomskii A.O.3
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Afiliações:
- Steklov Mathematical Institute of Russian Academy of Sciences
- University of Illinois at Urbana-Champaign
- National Research University Higher School of Economics
- Edição: Volume 215, Nº 5 (2024)
- Páginas: 47-70
- Seção: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/255924
- DOI: https://doi.org/10.4213/sm9980
- ID: 255924
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Resumo
Для натурального $n$ обозначим через $F(n)$ расстояние от $n$ до ближайшего простого числа. Используя метод из недавней работы К. Форда, C. Конягина, Дж. Мейнарда, К. Померанса и Т. Тао “Long gaps in sieved sets” (J. Eur. Math. Soc., 23:2 (2021), 667–700), мы доказываем, что всякое достаточно большое натуральное $N$ может быть представлено в виде $N=n_1+n_2$, где $F(n_i) \geqslant (\log N)(\log\log N)^{1/325565}$, для $i=1,2$. Данный результат улучшает аналогичный “тривиальный” результат с условием вида $F(n_i)\gg \log N$. Библиография: 17 названий.
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Sobre autores
Mikhail Gabdullin
Steklov Mathematical Institute of Russian Academy of Sciences; University of Illinois at Urbana-Champaign
Email: gabdullin@mi-ras.ru
Scopus Author ID: 57190070116
Candidate of physico-mathematical sciences
Artyom Radomskii
National Research University Higher School of Economics
Email: artyom.radomskii@mail.ru
ORCID ID: 0000-0002-2675-2134
Scopus Author ID: 37116185600
Researcher ID: Q-4513-2016
Candidate of physico-mathematical sciences, Researcher
Bibliografia
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