Twin, cousin, and sexy prime counting function. Explicit formulas
UDC 511 We give explicit formulas for the twin-prime and cousin-prime counting functions. We propose a formula that computes the number of primes less than or equal to $n$  whose difference is $m\geqslant 6.$ We also present a characterization specifying when t...
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| Date: | 2024 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7567 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512685241663488 |
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| author | Kowitz, Krzysztof Kowitz, Krzysztof |
| author_facet | Kowitz, Krzysztof Kowitz, Krzysztof |
| author_sort | Kowitz, Krzysztof |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-02-11T07:15:16Z |
| description | UDC 511
We give explicit formulas for the twin-prime and cousin-prime counting functions. We propose a formula that computes the number of primes less than or equal to $n$  whose difference is $m\geqslant 6.$ We also present a characterization specifying when two numbers whose difference is $n\geqslant 2$ are primes. |
| doi_str_mv | 10.3842/umzh.v76i8.7567 |
| first_indexed | 2026-03-24T03:32:43Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7567 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:43Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-75672025-02-11T07:15:16Z Twin, cousin, and sexy prime counting function. Explicit formulas Twin, cousin, and sexy prime counting function. Explicit formulas Kowitz, Krzysztof Kowitz, Krzysztof prime numbers, twin prime numbers, cousin prime numbers, sexy prime numbers, counting function. UDC 511 We give explicit formulas for the twin-prime and cousin-prime counting functions. We propose a formula that computes the number of primes less than or equal to $n$  whose difference is $m\geqslant 6.$ We also present a characterization specifying when two numbers whose difference is $n\geqslant 2$ are primes. УДК 511 Функція підрахунку простих чисел, що відрізняються на два, чотири або шість. Явні формули Наведено явні формули для функцій підрахунку простих чисел, що відрізняються на два або чотири. Дано формулу, що визначає кількість простих чисел із різницею $m\geqslant 6,$ які менші або рівні $n.$ Запропоновано також характеристику, за якої два числа з різницею $n\geqslant 2$ є простими. Institute of Mathematics, NAS of Ukraine 2024-09-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7567 10.3842/umzh.v76i8.7567 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 8 (2024); 1260 - 1264 Український математичний журнал; Том 76 № 8 (2024); 1260 - 1264 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7567/10160 Copyright (c) 2024 Krzysztof Kowitz |
| spellingShingle | Kowitz, Krzysztof Kowitz, Krzysztof Twin, cousin, and sexy prime counting function. Explicit formulas |
| title | Twin, cousin, and sexy prime counting function. Explicit formulas |
| title_alt | Twin, cousin, and sexy prime counting function. Explicit formulas |
| title_full | Twin, cousin, and sexy prime counting function. Explicit formulas |
| title_fullStr | Twin, cousin, and sexy prime counting function. Explicit formulas |
| title_full_unstemmed | Twin, cousin, and sexy prime counting function. Explicit formulas |
| title_short | Twin, cousin, and sexy prime counting function. Explicit formulas |
| title_sort | twin, cousin, and sexy prime counting function. explicit formulas |
| topic_facet | prime numbers twin prime numbers cousin prime numbers sexy prime numbers counting function. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7567 |
| work_keys_str_mv | AT kowitzkrzysztof twincousinandsexyprimecountingfunctionexplicitformulas AT kowitzkrzysztof twincousinandsexyprimecountingfunctionexplicitformulas |