Result Details
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. 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×. 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.
Collatz conjecture, software optimization, parallel computing, number theory
@article{BUT197809,
author="David {Bařina}",
title="Improved verification limit for the convergence of the Collatz conjecture",
journal="JOURNAL OF SUPERCOMPUTING",
year="2025",
volume="81",
number="1",
pages="1--14",
doi="10.1007/s11227-025-07337-0",
issn="0920-8542",
url="https://link.springer.com/article/10.1007/s11227-025-07337-0"
}