## Abstract

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.

Along the way, we prove that the level of distribution of the Zeckendorf sum-of-digits function equals 1.

Translated title of the contribution | Darstellung von Primzahlen als Summe von Fibonacci-Zahlen |
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Original language | English |

Number of pages | 135 |

Journal | Memoirs of the American Mathematical Society |

Publication status | Accepted/In press - 1 Sept 2022 |

## Keywords

- prime numbers
- Fibonacci numbers
- level of distribution