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 |
| Published: |
New York
Springer Nature B.V
02.05.2025
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| Subjects: | |
| ISSN: | 1573-0484, 0920-8542, 1573-0484 |
| Online Access: | Get full text |
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| Summary: | 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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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1573-0484 0920-8542 1573-0484 |
| DOI: | 10.1007/s11227-025-07337-0 |