Recent Results on Large Gaps Between Primes
One of the themes of this paper is recent results on large gaps between primes. The first of these results was achieved in the paper by Ford, Green, Konyagin and Tao. It was later improved in the joint paper of these four authors with Maynard. One of the main ingredients of these results is old meth...
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2025-03-01
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| author | Michael Th. Rassias |
| author_facet | Michael Th. Rassias |
| author_sort | Michael Th. Rassias |
| collection | DOAJ |
| description | One of the themes of this paper is recent results on large gaps between primes. The first of these results was achieved in the paper by Ford, Green, Konyagin and Tao. It was later improved in the joint paper of these four authors with Maynard. One of the main ingredients of these results is old methods from Erdős and Rankin. Other ingredients are important breakthrough results from Goldston, Pintz and Yildirim, and their extension by Maynard on small gaps between primes. All these previous results are discussed in brief. The results on the appearance of <i>k</i>-th powers of primes contained in those large gaps obtained by the author in joint work with Maier are based on a combination of the results just described with the matrix method of Maier. |
| format | Article |
| id | doaj-art-c6e65a10e1134965a601d7ab12714a9f |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-c6e65a10e1134965a601d7ab12714a9f2025-08-20T03:43:02ZengMDPI AGAxioms2075-16802025-03-0114319810.3390/axioms14030198Recent Results on Large Gaps Between PrimesMichael Th. Rassias0Department of Mathematics and Engineering Sciences, Hellenic Military Academy, 16673 Vari Attikis, GreeceOne of the themes of this paper is recent results on large gaps between primes. The first of these results was achieved in the paper by Ford, Green, Konyagin and Tao. It was later improved in the joint paper of these four authors with Maynard. One of the main ingredients of these results is old methods from Erdős and Rankin. Other ingredients are important breakthrough results from Goldston, Pintz and Yildirim, and their extension by Maynard on small gaps between primes. All these previous results are discussed in brief. The results on the appearance of <i>k</i>-th powers of primes contained in those large gaps obtained by the author in joint work with Maier are based on a combination of the results just described with the matrix method of Maier.https://www.mdpi.com/2075-1680/14/3/198large gaps between primesErdős-Rankin methodsmall gaps between primesmaier matrix methodsieve methods |
| spellingShingle | Michael Th. Rassias Recent Results on Large Gaps Between Primes Axioms large gaps between primes Erdős-Rankin method small gaps between primes maier matrix method sieve methods |
| title | Recent Results on Large Gaps Between Primes |
| title_full | Recent Results on Large Gaps Between Primes |
| title_fullStr | Recent Results on Large Gaps Between Primes |
| title_full_unstemmed | Recent Results on Large Gaps Between Primes |
| title_short | Recent Results on Large Gaps Between Primes |
| title_sort | recent results on large gaps between primes |
| topic | large gaps between primes Erdős-Rankin method small gaps between primes maier matrix method sieve methods |
| url | https://www.mdpi.com/2075-1680/14/3/198 |
| work_keys_str_mv | AT michaelthrassias recentresultsonlargegapsbetweenprimes |