Publication detail
Improved verification limit for the convergence of the Collatz conjecture
BAŘINA, D.
Original Title
Improved verification limit for the convergence of the Collatz conjecture
Type
journal article in Web of Science
Language
English
Original 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.
Keywords
Collatz conjecture, software optimization, parallel computing, number theory
Authors
BAŘINA, D.
Released
2. 5. 2025
ISBN
1573-0484
Periodical
Journal of Supercomputing
Year of study
81
Number
1
State
United States of America
Pages from
1
Pages to
14
Pages count
14
URL
BibTex
@article{BUT197809,
author="David {Bařina}",
title="Improved verification limit for the convergence of the Collatz conjecture",
journal="Journal of Supercomputing",
year="2025",
volume="81",
number="1",
pages="1--14",
doi="10.1007/s11227-025-07337-0",
issn="1573-0484",
url="https://link.springer.com/article/10.1007/s11227-025-07337-0"
}Documents