Collatz Conjecture: Is It False?

TL;DR

This paper presents evidence and an algorithm suggesting that the Collatz Conjecture is false, indicating the existence of integers with non-finite stopping times, contrary to long-held assumptions.

Contribution

It introduces a pattern analysis of stopping times and a non-halting algorithm that challenge the assumption of the conjecture's truth.

Findings

Pattern of infinite stopping times identified

Algorithm finds integers with arbitrarily large stopping times

Evidence suggests the conjecture is false

Abstract

For a long time, Collatz Conjecture has been assumed to be true, although a formal proof has eluded all efforts to date. In this article, evidence is presented that suggests such an assumption is incorrect. By analysing the stopping times of various Collatz sequences, a pattern emerges that indicates the existence of non-empty sets of integers with stopping times greater than any given integer. This implies the existence of an infinite set of integers with non-finite stopping times, thus indicating the conjecture is false. Furthermore, a simple algorithm is constructed that finds integers with ever-greater stopping times. Such an algorithm does not halt, further supporting the conclusion that the conjecture is false.