Computational Verification of the Collatz Problem

Computational Verification of the Collatz Problem | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Computational Verification of the Collatz Problem David Barina This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3845558/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 3 You are reading this latest preprint version Abstract This article presents our project, which aims to verify the convergence of the Collatz problem computationally. As a main point of the article, we introduce a new result that pushes the limit for which the problem is verified up to 1.5 × 270. We present our baseline algorithm and then several sub-algorithms that bring some 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. Collatz conjecture Software optimization Parallel computing Number theory Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editor assigned by journal 09 Jan, 2024 Submission checks completed at journal 09 Jan, 2024 First submitted to journal 08 Jan, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3845558","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266120934,"identity":"7ddc74d7-b06a-4bd7-b6fe-86d29923cdf5","order_by":0,"name":"David Barina","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1klEQVRIiWNgGAWjYBACNgkgkcDAIMfeDBFIIFqLMc9hZhDfgLAWBgkIldhzgFgtfNLNzz483GGX3sPOf4CZt+1PnnkD8+MPeB0mc8x4RuKZ5NweZmYGoBaDYpkDbAYG+P2SYMyQ2Macux+ohXFmm0HiDAYe/GHAJpH+GailPp0HWcsB/FpyQLYcTgBpYfgI0cLYgN8vZ4qBWo4bAv1icODDOeNiCWY2Y3w6GORnt29m/NlWLc/Df/Dhg4QyuTwJ9mb8IYYCIF5gJlr9KBgFo2AUjAJcAADjDDwRNv314QAAAABJRU5ErkJggg==","orcid":"","institution":"Brno University of Technology","correspondingAuthor":true,"prefix":"","firstName":"David","middleName":"","lastName":"Barina","suffix":""}],"badges":[],"createdAt":"2024-01-08 13:59:11","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3845558/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3845558/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49449565,"identity":"40f04757-3e03-4085-9f05-da31c3d7838d","added_by":"auto","created_at":"2024-01-11 04:13:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":167793,"visible":true,"origin":"","legend":"","description":"","filename":"r1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3845558/v1_covered_91531b52-2a95-44f6-99fa-2e7422b2cd72.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Computational Verification of the Collatz Problem","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Collatz conjecture, Software optimization, Parallel computing, Number theory","lastPublishedDoi":"10.21203/rs.3.rs-3845558/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3845558/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This article presents our project, which aims to verify the convergence of the Collatz problem computationally. 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