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"
}

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