Unconditional Prime-Representing Functions, Following Mills

Christian Elsholtz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Mills proved that there exists a real constant A > 1 such that for all (Formula presented.) the values (Formula presented.) are prime numbers. No explicit value of A is known, but assuming the Riemann hypothesis one can choose (Formula presented.) Here we give a first unconditional variant: (Formula presented.) is prime, where (Formula presented.) can be computed to millions of digits. Similarly, (Formula presented.) is prime, with (Formula presented.).

Original languageEnglish
Pages (from-to)639-642
Number of pages4
JournalThe American Mathematical Monthly
Issue number7
Publication statusPublished - 8 Aug 2020


  • MSC: Primary 11A41
  • Secondary 11N05

ASJC Scopus subject areas

  • Mathematics(all)

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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