Odd perfect numbers have a prime factor exceeding 10

Takeshi Goto, Yasuo Ohno

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding 107. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding 108.

Original languageEnglish
Pages (from-to)1859-1868
Number of pages10
JournalMathematics of Computation
Volume77
Issue number263
DOIs
Publication statusPublished - 2008 Jul
Externally publishedYes

Keywords

  • Cyclotomic numbers
  • Odd perfect numbers

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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