English

An improved algorithm for checking the Collatz conjecture for all n < 2^N

Number Theory 2026-02-12 v1

Abstract

We describe a new algorithm for verifying the Collatz conjecture for all n < 2^N for some fixed N. The algorithm takes less than twice as long to verify convergence for all n < 2^{N+1} as it does to verify convergence for all n < 2^N. We also discuss verification of the analogue of the Collatz conjecture for negative numbers.

Keywords

Cite

@article{arxiv.2602.10466,
  title  = {An improved algorithm for checking the Collatz conjecture for all n < 2^N},
  author = {Vigleik Angeltveit},
  journal= {arXiv preprint arXiv:2602.10466},
  year   = {2026}
}

Comments

Comments very welcome

R2 v1 2026-07-01T10:31:06.593Z