Almost arithmetic progressions in the primes and other large sets
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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.
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
The American Mathematical Monthly
Copyright © 2019 The Mathematical Association of America. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1080/00029890.2019.1586264
DescriptionFunding: The author is financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1).
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