Primes with preassigned digits
Glyn Harman (2006)
Acta Arithmetica
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Glyn Harman (2006)
Acta Arithmetica
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M. C. Liu, T. Z. Wang (2002)
Acta Arithmetica
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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.
Gustavo Funes, Damian Gulich, Leopoldo Garavaglia, Mario Garavaglia (2008)
Visual Mathematics
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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.
Glyn Harman, Imre Kátai (2008)
Acta Arithmetica
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Hongze Li (2001)
Acta Arithmetica
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Kaisa Matomäki (2009)
Acta Arithmetica
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Yingchun Cai, Minggao Lu (2003)
Acta Arithmetica
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Christian Elsholtz (2003)
Acta Arithmetica
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Jan Mycielski (1989)
Colloquium Mathematicae
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Dieter Wolke (2005)
Acta Arithmetica
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Antal Balog (1985)
Banach Center Publications
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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.
Yuan Wang (1978-1979)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
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Hakan Ali-John Seyalioglu (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.
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).
Zhixin Liu, Guangshi Lü (2010)
Acta Arithmetica
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