Detail publikačního výsledku

Improved verification limit for the convergence of the Collatz conjecture

BAŘINA, D.

Originální název

Improved verification limit for the convergence of the Collatz conjecture

Anglický název

Improved verification limit for the convergence of the Collatz conjecture

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Collatz conjecture, software optimization, parallel computing, number theory

Klíčová slova v angličtině

Collatz conjecture, software optimization, parallel computing, number theory

Autoři

BAŘINA, D.

Vydáno

02.05.2025

ISSN

1573-0484

Periodikum

JOURNAL OF SUPERCOMPUTING

Svazek

81

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

14

Strany počet

14

URL

https://link.springer.com/article/10.1007/s11227-025-07337-0

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="0920-8542",
  url="https://link.springer.com/article/10.1007/s11227-025-07337-0"
}

Dokumenty

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