Improved verification limit for the convergence of the Collatz conjecture
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 $$2^{71}$$ 2 71 . We present our baseline algorithm and then several sub-algorith...
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| Published in: | The Journal of supercomputing Vol. 81; no. 7; p. 810 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
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New York
Springer Nature B.V
02.05.2025
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| ISSN: | 1573-0484, 0920-8542, 1573-0484 |
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| 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 $$2^{71}$$ 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 $$1\,335\times$$ 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. |
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| AbstractList | 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 271. 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 1335×. 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. 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 $$2^{71}$$ 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 $$1\,335\times$$ 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. |
| ArticleNumber | 810 |
| Author | Barina, David |
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| Cites_doi | 10.1016/0898-1221(92)90034-F 10.1214/aoap/1177005779 10.1090/S0025-5718-99-01031-5 10.1090/mbk/078 10.1007/s11227-020-03368-x |
| ContentType | Journal Article |
| Copyright | The Author(s) 2025. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| References | R Dunn (7337_CR5) 1973 C Hercher (7337_CR12) 2023; 26 TOE Silva (7337_CR11) 1999; 68 GT Leavens (7337_CR6) 1992; 24 7337_CR7 7337_CR8 7337_CR9 D Barina (7337_CR4) 2021; 77 JC Lagarias (7337_CR13) 1992; 2 7337_CR1 7337_CR2 7337_CR3 T Honda (7337_CR10) 2017; 7 |
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| Title | Improved verification limit for the convergence of the Collatz conjecture |
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