Trace individual trajectories and exhaustively verify ranges of integers — the same kind of empirical search researchers run, just in your browser tab.
The Collatz conjecture claims that repeatedly applying one rule to any positive integer always eventually reaches 1. It is unproven — nobody has found a counterexample, and nobody has proven one can't exist. It does what every computer-assisted attempt on it has done: run the rule and watch what happens.
n is even → n / 2
n is odd → 3n + 1
repeat until n = 1
Scan every integer in a range and confirm each one reaches 1, tracking the longest trajectories and highest peaks found. Runs in a background thread so the page stays responsive.
| Starting number | Steps |
|---|
| Starting number | Peak value |
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Enter any positive integer (as large as you like) and watch its trajectory, a.k.a. "hailstone sequence."