Some Applications of the Maynard-Tao Theorem

Some Applications of the Maynard-Tao Theorem

Let and be the set of natural numbers and prime numbers, respectively. For a positive integer n, define the following two representation functions and An old result of Erdős showed that is unbounded. As an elementary application of the Maynard-Tao theorem, we prove that is also unbounded, which conf...

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Veröffentlicht in:The American mathematical monthly 2023-07, Vol.130 (6), p.583-586
Hauptverfasser: Ding, Yuchen, Zhou, Guang-Liang
Format: Artikel
Sprache:eng
Schlagworte:
Integer programming
Mathematical functions
Mathematics
Number theory
Prime numbers
Theorems
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Zusammenfassung:Let and be the set of natural numbers and prime numbers, respectively. For a positive integer n, define the following two representation functions and An old result of Erdős showed that is unbounded. As an elementary application of the Maynard-Tao theorem, we prove that is also unbounded, which confirms a conjecture of Chen in 2010.
ISSN:0002-9890
1930-0972
DOI:10.1080/00029890.2023.2184621