Infinite Collatz
The simplest unsolved question
$1.99 · Designed for iPad. Not verified for macOS.
Pick a number. Even? Halve it. Odd? Triple it and add one. Repeat. Every number ever tried leads to 1, but nobody can prove they all do (or don't). Watch your phone try.
Pick a whole number, any whole number. If it's even, halve it. If it's odd, triple it and add one. Now do the same to the answer, and keep going. In 1937 the German mathematician Lothar Collatz suggested that, whatever number you start with, you always end up at 1. Computers have checked every number up to 2⁷¹, about 2.4 sextillion, and every single one gets there. But no one has been able to prove it for all numbers (or disprove it with a number that doesn’t).
Infinite Collatz checks the numbers one after another, as fast as your iPhone or iPad can manage, and shows you some fascinating ways of visualizing what it finds.
HOW IT WORKS
Press 'Start'. Your device calculates each number’s sequence, all the way down to 1, and keeps a record as it goes. Choose slow, medium or fast in Settings to watch each sequence go by, or let it race through millions. We recommend enjoying some of the visualizations in slow or medium.
WHAT YOU SEE
• The number being checked and its sequence.
• The longest sequence so far: the number that takes the most steps to reach 1.
• Six visualizations:
– Current sequence: the number being checked, step by step down to 1, with its peak in red.
– Log: every number checked, with its steps and peak. Tap any row to see its sequence in full.
– Stopping times: every number against the steps it takes to reach 1, with the average.
– Frequencies: how many numbers take each number of steps.
– Peaks: how high each number climbs before it falls back to 1.
– Corals: the routes of the first 5,000 numbers, drawn back from 1, turning one way on each halving and the other way on each 3n + 1, so shared routes grow into branches. Move the sliders to change the angle of the turns.
EXACT TO THE LAST DIGIT
Some sequences climb astonishingly high: 704,511 reaches 56,991,483,520 before falling back to 1. Infinite Collatz keeps every value exact, however large it gets.
SIMPLE AND PRIVATE
No ads, no account, no in-app purchases, and nothing leaves your device. It checks numbers while the app is open and carries on where it left off. It slows down when your device is warm or in Low Power Mode, and stops if it gets hot.
Terms of Use: https://eruscape.com/terms/
Privacy Policy: https://eruscape.com/privacy/
Ratings & Reviews
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The developer, Eruscape Digital Ltd, indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .
Data Not Collected
The developer does not collect any data from this app.
Accessibility
The developer has not yet indicated which accessibility features this app supports. Learn More
Information
- Seller
- Eruscape Digital Ltd
- Size
- 50.8 MB
- Category
- Entertainment
- Compatibility
Requires iOS 16.4 or later.
- iPhone
Requires iOS 16.4 or later. - iPad
Requires iPadOS 16.4 or later. - Mac
Requires macOS 12.0 or later and a Mac with Apple M1 chip or later. - Apple Vision
Requires visionOS 1.0 or later.
- iPhone
- Languages
- English
- Age Rating
18+
- 18+
- Copyright
- © 2026 Eruscape Digital Ltd
