Detecting squarefree numbers

Andrew R Booker, Ghaith Hiary, Jon P Keating

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

2 Citations (Scopus)
317 Downloads (Pure)


We present an algorithm, based on the explicit formula for L-functions and conditional on the generalized Riemann hypothesis, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically and use it to prove that several RSA challenge numbers are not squarefull.

Original languageEnglish
Pages (from-to)235-275
Number of pages41
JournalDuke Mathematical Journal
Issue number2
Publication statusPublished - 30 Jan 2015


  • 11Y16: Algorithms; complexity [See also 68Q25]
  • 11M06: ζ(s) and L(s,χ)
  • 11Y35: Analytic computations
  • 11M50: Relations with random matrices


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