Convergence verification of the Collatz problem

  title={Convergence verification of the Collatz problem},
  author={David Barina},
  journal={The Journal of Supercomputing},
  • David Barina
  • Published 1 July 2020
  • Computer Science, Mathematics
  • The Journal of Supercomputing
This article presents a new algorithmic approach for computational convergence verification of the Collatz problem. The main contribution of the paper is the replacement of huge precomputed tables containing $$O(2^N)$$ O ( 2 N ) entries with small lookup tables comprising just O ( N ) elements. Our single-threaded CPU implementation can verify $$4.2 \times 10^9$$ 4.2 × 10 9 128-bit numbers per second on Intel Xeon Gold 5218 CPU computer, and our parallel OpenCL implementation reaches the speed… 

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