Email this article Prime avoiding numbers is a basis of order 2
- Authors: Gabdullin M.R.1,2, Radomskii A.O.3
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- University of Illinois at Urbana-Champaign
- National Research University Higher School of Economics
- Issue: Vol 215, No 5 (2024)
- Pages: 47-70
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/255924
- DOI: https://doi.org/10.4213/sm9980
- ID: 255924
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Abstract
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.
Keywords
About the authors
Mikhail Rashidovich 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 Olegovich Radomskii
National Research University Higher School of Economics
Email: artyom.radomskii@mail.ru
ORCID iD: 0000-0002-2675-2134
Scopus Author ID: 37116185600
ResearcherId: Q-4513-2016
Candidate of physico-mathematical sciences, Researcher
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