Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Sprache: | Englisch |
| Veröffentlicht: |
Zenodo
2025
|
| Schlagworte: | |
| Online-Zugang: | https://doi.org/10.5281/zenodo.15314038 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Inhaltsangabe:
- <p>We prove that there are only finitely many prime values in the base-10 repunit<br>sequence<br>Rn = (10n − 1)/9 .<br>Our proof relies purely on structural properties of repunits, combining cyclotomic<br>factorization, growth of primitive prime divisors via Zsigmondy’s Theorem, and sym-<br>bolic entropy compression arguments. We show that as n → ∞, the redundancy and<br>multiplicative structure of Rn necessarily force compositeness beyond a finite bound,<br>independent of computational residue checks.</p> <p><br>By analyzing the entropy structure of repeated-digit numbers and the accumulation<br>of distinct prime divisors, we demonstrate that repunit primes must be confined to<br>finitely many small indices. The result is a complete classical proof confirming the<br>longstanding conjecture that only finitely many base-10 repunit numbers are prime.</p>