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Almost arithmetic progressions in the primes and other large sets

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  • Embargoed (until 29/05/20)

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Abstract

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.
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Original languageEnglish
Pages (from-to)553-558
Number of pages6
JournalThe American Mathematical Monthly
Volume126
Issue number6
Early online date29 May 2019
DOIs
Publication statusPublished - May 2019

    Research areas

  • Arithmetic progression, Primes, Green-Tao Theorem, Erdős-Turan Conjecture

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