Problem

Source of collatz-conjecture

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---
title: Collatz conjecture
kind: problem
status: open
year: 1937
authors: Lothar Collatz
statement: Halving even numbers and sending odd n to 3n + 1 always reaches 1.
space: number-theory
---

A child can run it and nobody can prove it. Terence Tao showed in 2019 that almost all orbits reach almost bounded values, the strongest result so far. Conway showed that natural generalizations are undecidable, which hints that the specific numbers 3 and 1 matter. A counterexample would be a number a computer can check, which makes this one of the few famous problems where a finite search could still end it.

Posed 1937, Lothar Collatz.

## What would settle it

Lean statement in formal-conjectures

## Sources

- [Wikipedia: Collatz conjecture](https://en.wikipedia.org/wiki/Collatz_conjecture)

[[Space:number-theory|Number theory]] · [[Continent:mathematics|Mathematics]]

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Syntax

Markdown, with $…$ math, [[Page]] links, typed relations [[implies::Statement:x|label]] inside the sentence that argues them (relations: implies, equivalent-to, special-case-of, reduces-to, proves, refutes, bounded-by, uses, formalizes, answers, witnesses, instance-of, related), index maps {{at|2n→n}}, references <ref>…</ref>, and figures: {{ladder|A|B}}, a ```region block, {{checker|name}}. Front matter between --- lines sets title, short, kind, status, tier, year, authors, statement, formal, scope, index, cells, stable. Full guide: Atlas:Help.