On the first sign change of θ(x)-x

David J Platt, Tim Trudgian

Research output: Contribution to journalArticle (Academic Journal)peer-review

21 Citations (Scopus)
251 Downloads (Pure)


Let θ(x) = ∑pxlogp. We show that θ(x) < x for 2 < x < 1.39·1017. We also show that there is an x < exp(727.951332668) for which θ(x) > x.
Original languageEnglish
Pages (from-to)1539-1547
Number of pages9
JournalMathematics of Computation
Publication statusPublished - 21 Aug 2015


  • Sign changes of arithmetical functions
  • oscillation theorems


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  • HPC (High Performance Computing) Facility

    Susan L Pywell (Manager), Simon A Burbidge (Other), Polly E Eccleston (Other) & Simon H Atack (Other)

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