Collatz Conjecture Calculator
Halve if even, triple and add one if odd. Nobody knows why it works.
Work out Collatz Conjecture. Halve if even, triple and add one if odd. Nobody knows why it works. Names the misconception directly.
Steps to reach 1
111
Peaking at 9,232
The rule is trivial — halve if even, triple and add one if odd — and the behaviour is not. Every starting value ever tested reaches 1, and nobody has proved that all of them do. It is one of the most famous open problems in mathematics, and Paul Erdős said of it that mathematics is not yet ready for such problems. 27 is the standard demonstration: it takes 111 steps and climbs to 9,232 before coming down, which is why small starting numbers are no guide to how long the sequence runs. The step ceiling here is a safety bound on the computation, not a statement about the conjecture. Nothing in the tested range comes close to it.
How the Collatz Conjecture Calculator works
Run any starting number through the Collatz rule and see the sequence, the step count and the peak. Every number ever tested reaches 1, and nobody has proved that all of them do — it remains one of the most famous open problems in mathematics.
Also known as: 3n plus 1 problem · hailstone numbers · collatz steps for 27 · does every number reach 1
Frequently asked questions
What is the Collatz conjecture?
The claim that starting from any positive integer, repeatedly halving if even and tripling-plus-one if odd always reaches 1. It has been verified far beyond 2^68 by computer and proved for exactly no numbers in general.
Why is 27 the standard example?
Because it takes 111 steps and climbs to 9,232 before descending. It shows plainly that a small starting number tells you nothing about how long the sequence runs or how high it goes.
Why is it called the hailstone sequence?
Because the values rise and fall repeatedly before settling, like hailstones carried up and down inside a storm cloud before finally falling. The name describes the graph better than any formal description does.
Has anyone proved it?
No. Terence Tao proved in 2019 that almost all starting values eventually reach a small number, which is the strongest partial result so far and still short of the conjecture. Erdős remarked that mathematics is not yet ready for such problems.
Is there a reward for solving it?
Various prizes have been offered over the years, and none has been claimed. The problem is famous partly because it is trivially easy to state and has resisted every technique brought against it for nearly a century.
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