Primes as Sums of Fibonacci Numbers

Lukas Spiegelhofer, Michael Drmota, Clemens Müllner

Research output: Contribution to journalArticleResearchpeer-review


We prove that, for a large enough integer k, there exist prime numbers that are the sum of exactly k different, non-consecutive Fibonacci numbers.
Along the way, we prove that the level of distribution of the Zeckendorf sum-of-digits function equals 1.
Translated title of the contributionDarstellung von Primzahlen als Summe von Fibonacci-Zahlen
Original languageEnglish
Number of pages135
JournalMemoirs of the American Mathematical Society
Publication statusAccepted/In press - 1 Sept 2022


  • prime numbers
  • Fibonacci numbers
  • level of distribution

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