Improved verification limit for the convergence of the Collatz conjecture

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26230%2F25%3APU156349" target="_blank" >RIV/00216305:26230/25:PU156349 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007/s11227-025-07337-0" target="_blank" >https://link.springer.com/article/10.1007/s11227-025-07337-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11227-025-07337-0" target="_blank" >10.1007/s11227-025-07337-0</a>

Result language

angličtina

Original language name

Improved verification limit for the convergence of the Collatz conjecture

Original language description

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.

Czech name

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Czech description

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Type

J_ost - Miscellaneous article in a specialist periodical

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Supercomputing

ISSN

0920-8542

e-ISSN

1573-0484

Volume of the periodical

81

Issue of the periodical within the volume

1

Country of publishing house

US - UNITED STATES

Number of pages

14

Pages from-to

1-14

UT code for WoS article

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EID of the result in the Scopus database

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