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