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dc.contributor.authorFraser, Jonathan M.
dc.identifier.citationFraser , J M 2019 , ' Almost arithmetic progressions in the primes and other large sets ' , The American Mathematical Monthly , vol. 126 , no. 6 , pp. 553-558 .
dc.identifier.otherPURE: 256233949
dc.identifier.otherPURE UUID: fb2f0206-54e9-49be-930f-96f8f8bc2b3e
dc.identifier.otherORCID: /0000-0002-8066-9120/work/58984319
dc.identifier.otherScopus: 85067059096
dc.identifier.otherWOS: 000470894300008
dc.descriptionFunding: The author is financially supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and an EPSRC Standard Grant (EP/R015104/1).en
dc.description.abstractA 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.
dc.relation.ispartofThe American Mathematical Monthlyen
dc.rightsCopyright © 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
dc.subjectArithmetic progressionen
dc.subjectGreen-Tao Theoremen
dc.subjectErdős-Turan Conjectureen
dc.subjectQA Mathematicsen
dc.titleAlmost arithmetic progressions in the primes and other large setsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews.Pure Mathematicsen
dc.description.statusPeer revieweden

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