Publication Details

Improved verification limit for the convergence of the Collatz conjecture

BAŘINA David. Improved verification limit for the convergence of the Collatz conjecture. The Journal of Supercomputing, vol. 81, no. 1, 2025, pp. 1-14. ISSN 1573-0484. Available from: https://link.springer.com/article/10.1007/s11227-025-07337-0
Czech title
Zlepšená mez, pod kterou Collatzova domněnka konverguje
Type
journal article
Language
english
Authors
Bařina David, Ing., Ph.D. (DCGM FIT BUT)
URL
Keywords

Collatz conjecture, software optimization, parallel computing, number theory

Abstract

This article presents our project, which aims to verify the Collatz conjecture computationally. As a main point of the article, we introduce a new result that pushes the limit for which the conjecture is verified up to 2^71. We present our baseline algorithm and then several sub-algorithms that enhance acceleration. The total acceleration from the first algorithm we used on the CPU to our best algorithm on the GPU is 1 335×. We further distribute individual tasks to thousands of parallel workers running on several European supercomputers. Besides the convergence verification, our program also checks for path records during the convergence test. We found four new path records.

Published
2025
Pages
1-14
Journal
The Journal of Supercomputing, vol. 81, no. 1, ISSN 1573-0484
Publisher
Springer Verlag
DOI
10.1007/s11227-025-07337-0
BibTeX 
@ARTICLE{FITPUB13509,
   author = "David Ba\v{r}ina",
   title = "Improved verification limit for the convergence of the Collatz conjecture",
   pages = "1--14",
   journal = "The Journal of Supercomputing",
   volume = 81,
   number = 1,
   year = 2025,
   ISSN = "1573-0484",
   doi = "10.1007/s11227-025-07337-0",
   language = "english",
   url = "https://www.fit.vut.cz/research/publication/13509"
}
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