On the largest prime factor of the mersenne numbers

Kevin Ford, Florian Luca, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review


Let P(k) be the largest prime factor of the positive integer k. In this paper, we prove that the series ∑n≥1 (log n)α /{P(2 n-1) is convergent for each constant <1/2, which gives a more precise form of a result of C. L.Stewart [On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers, Proc. London Math. Soc. 35(3) (1977), 425-447].

Original languageEnglish (US)
Pages (from-to)455-463
Number of pages9
JournalBulletin of the Australian Mathematical Society
Issue number3
StatePublished - Jun 2009


  • Mersenne numbers
  • applications of sieve methods
  • primes

ASJC Scopus subject areas

  • General Mathematics


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