Unconditional Prime-Representing Functions, Following Mills

Christian Elsholtz

doi:10.1080/00029890.2020.1751560

Unconditional Prime-Representing Functions, Following Mills

Christian Elsholtz^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	639-642
Number of pages	4
Journal	The American Mathematical Monthly
Volume	127
Issue number	7
DOIs	https://doi.org/10.1080/00029890.2020.1751560
Publication status	Published - 8 Aug 2020

Keywords

MSC: Primary 11A41
Secondary 11N05

ASJC Scopus subject areas

General Mathematics

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

Access to Document

10.1080/00029890.2020.1751560

Cite this

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KW - Secondary 11N05

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Unconditional Prime-Representing Functions, Following Mills

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Treatment code (Nähere Zuordnung)

Access to Document

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