Almost arithmetic progressions in the primes and other large sets
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Date
05/2019Author
Grant ID
RF-2016-500
EP/R015104/1
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A celebrated and deep result of Green and Tao states that the primes contain arbitrarily long arithmetic progressions. In this note, I provide a straightforward argument demonstrating that the primes get arbitrarily close to arbitrarily long arithmetic progressions. The argument also applies to “large sets” in the sense of the Erdős conjecture on arithmetic progressions. The proof is short, completely self-contained, and aims to give a heuristic explanation of why the primes, and other large sets, possess arithmetic structure.
Citation
Fraser , J M 2019 , ' Almost arithmetic progressions in the primes and other large sets ' , The American Mathematical Monthly , vol. 126 , no. 6 , pp. 553-558 . https://doi.org/10.1080/00029890.2019.1586264
Publication
The American Mathematical Monthly
Status
Peer reviewed
ISSN
0002-9890Type
Journal article
Description
Funding: The author is financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1).Collections
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