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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Main Author: Michael Th. Rassias
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/3/198
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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.
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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