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Improved verifcation limit for the convergence of the Collatz conjecture
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This article presents our project, which aims to verify the Collatz conjecture com- putationally. As a main point of the article, we introduce a new result that pushes the limit for which the conjecture is verifed up to 271. We present our baseline algo- rithm and then several sub-algorithms that enhance acceleration. The total accelera- tion from the frst 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 verifcation, our program also checks for path records during the convergence test. We found four new path records.
Collatz conjectureSoftware optimizationParallel computingNumber theory
David Barina
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Faculty of Information Technology, Brno University of Technology, Bozetechova 1/2, Brno, Czech Republic
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