Further results on a generalization of Bertrand's postulate
Let d(k) be defined as the least positive integer n for which pn+1<2pn−k. In this paper we will show that for k≥286664, then d(k)<k/(logk−2.531) and for k≥2, then k(1−1/logk)/logk<d(k). Furthermore, for k sufficiently large we establish upper and lower bounds for d(k).
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| Format: | Article |
| Language: | English |
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Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171296000129 |
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| _version_ | 1832563944933294080 |
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| author | George Giordano |
| author_facet | George Giordano |
| author_sort | George Giordano |
| collection | DOAJ |
| description | Let d(k) be defined as the least positive integer n for which pn+1<2pn−k. In this paper we will show that for k≥286664, then d(k)<k/(logk−2.531) and for k≥2, then k(1−1/logk)/logk<d(k). Furthermore, for k sufficiently large we establish upper and lower bounds for d(k). |
| format | Article |
| id | doaj-art-dc20a956306d4cc9991c12ee1b2c7778 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-dc20a956306d4cc9991c12ee1b2c77782025-02-03T01:12:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-01191758510.1155/S0161171296000129Further results on a generalization of Bertrand's postulateGeorge Giordano0Department of Mathematics, Physics and Computer Science, Ryerson Polytechnic University, Ontario, Toronto M5B 2K3, CanadaLet d(k) be defined as the least positive integer n for which pn+1<2pn−k. In this paper we will show that for k≥286664, then d(k)<k/(logk−2.531) and for k≥2, then k(1−1/logk)/logk<d(k). Furthermore, for k sufficiently large we establish upper and lower bounds for d(k).http://dx.doi.org/10.1155/S0161171296000129Bertrand's postulateprimes. |
| spellingShingle | George Giordano Further results on a generalization of Bertrand's postulate International Journal of Mathematics and Mathematical Sciences Bertrand's postulate primes. |
| title | Further results on a generalization of Bertrand's postulate |
| title_full | Further results on a generalization of Bertrand's postulate |
| title_fullStr | Further results on a generalization of Bertrand's postulate |
| title_full_unstemmed | Further results on a generalization of Bertrand's postulate |
| title_short | Further results on a generalization of Bertrand's postulate |
| title_sort | further results on a generalization of bertrand s postulate |
| topic | Bertrand's postulate primes. |
| url | http://dx.doi.org/10.1155/S0161171296000129 |
| work_keys_str_mv | AT georgegiordano furtherresultsonageneralizationofbertrandspostulate |