Live math · Collatz

Chasing 3n + 1.

My server checks every positive integer for the Collatz conjecture — an open problem since 1937 — tracking how far it has verified and the number with the longest journey to 1.

liveverifying every positive integer, one by one, forever

no loop up to

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every n reaches 1

longest trajectory

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steps to reach 1

record holder

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the number that took longest

total steps computed

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since boot

Hailstone trajectory

The value climbs and crashes unpredictably — “hailstones” in a cloud — yet always, so far, tumbles to 1. Vertical scale is log₂.

Try your own number

Computed in your browser with big integers — try 27, or 6171. Even a thousand-digit number works (the graph scales by bit-length).

How it works

The Collatz conjecture (1937): take any positive integer; if it's even, halve it; if odd, triple it and add one. Repeat. The claim is that you always reach 1 — but no one has proved it.

The server checks each integer in turn. Every one so far reaches 1 (that's the growing frontier), and it keeps the record for the most steps — a genuine, if quixotic, hunt for a counterexample.