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.