Primes with preassigned digits
Glyn Harman (2006)
Acta Arithmetica
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Glyn Harman (2006)
Acta Arithmetica
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Daniel Alan Goldston, János Pintz, Cem Yalçın Yıldırım (2013)
Acta Arithmetica
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We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η is given explicitly, providing a new quantitative way, in addition to that of the first paper in this series, of measuring the effect of the knowledge on the level of distribution of primes.
Gustavo Funes, Damian Gulich, Leopoldo Garavaglia, Mario Garavaglia (2008)
Visual Mathematics
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Glyn Harman, Imre Kátai (2008)
Acta Arithmetica
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Kaisa Matomäki (2009)
Acta Arithmetica
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Jörg Brüdern, Koichi Kawada (2011)
Colloquium Mathematicae
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A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.
Dieter Wolke (2005)
Acta Arithmetica
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Jan Mycielski (1989)
Colloquium Mathematicae
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Yingchun Cai, Minggao Lu (2003)
Acta Arithmetica
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Christian Elsholtz (2003)
Acta Arithmetica
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Roger C. Baker, Liangyi Zhao (2016)
Acta Arithmetica
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We study the gaps between primes in Beatty sequences following the methods in the recent breakthrough by Maynard (2015).
Enxun Huang (2023)
Czechoslovak Mathematical Journal
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It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.
Chaumont, Alain, Müller, Tom (2006)
Journal of Integer Sequences [electronic only]
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Akshaa Vatwani (2018)
Czechoslovak Mathematical Journal
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We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.
Hakan Ali-John Seyalioglu (2009)
Acta Arithmetica
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Müller, Tom (2006)
Experimental Mathematics
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Liqun Hu, Li Yang (2017)
Open Mathematics
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In this paper, we obtained that when k = 455, every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of 2.
Hongze Li, Hao Pan (2008)
Acta Arithmetica
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Gouvêa, Fernando Q. (1997)
Experimental Mathematics
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Zhixin Liu, Guangshi Lü (2010)
Acta Arithmetica
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