Many Paths of the Collatz Conjecture

The Collatz Conjecture is one of mathematics' strange unsolved problems. The rule is deceptively simple: take any positive integer, and if it's even divide it by 2, if it's odd multiply by 3 and add 1. Repeat this process and the sequence seems to always eventually reach 1. Always. This is true for every number ever tested! Even still, no one has ever been able to prove it, though some attempts have got close.

The sequences themselves are practically unpredictable. For example, the number 27 takes 111 steps while rocketing up to 9,232 before finally collapsing to 1. Nearby numbers can reach 1 in just a handful of steps, while others take hundreds of chaotic steps before converging. Use the interactive math tool below to explore and compare up to 5 numbers at once.

Collatz Conjecture Visualizer

Pick any positive integer. If it's even, divide by 2. If it's odd, multiply by 3 and add 1. Repeat. No matter what number you start with, the sequence always seems to reach 1, but nobody has ever proved why. Enter up to 5 numbers to compare their paths.

Enter Numbers to Compare

About the Collatz Conjecture: Mathematician Paul Erdős said: “Mathematics is not yet ready for such problems.”

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Express Your Message as Atomic Weights

The Element Cipher transforms your words into strings of element names and then converts those to numbers that are based on the atomic weights for those elements. It’s a fun little chemistry-themed encoder. Type a phrase and watch it translate into a sequence of elemental values that hides your message in plain sight. Decode it back and your text reappears from the atomic haze!

Element Cipher

Converts text to atomic masses (3-digit format) and back.

Message to Cipher/Decipher (English or 3-digit string)

Note on Numerals: Numerals (0-9) are not supported for encoding. Please spell out the words.

Cipher Output / Deciphered Result (Click or tap to copy)

Number and Word Converter Utility

 Need to quickly change a large number like 15,000,000 into its written form, or check the value of words for numbers that are verbosely spelled out? This simple bidirectional converter handles all your number-to-word and word-to-number needs for figures up to 999,999,999. It uses the U.S. standard (no hyphens, all lowercase) for word output. It's also designed to be very forgiving when you type words in, as it can handle extra spaces, mixed cases, and even words like "and" without reporting an error. Just paste a number or type out your phrase in the box. The result will instantly appear below. Tap the result box to copy the converted value.

Number & Word Converter

Enter Number (e.g., 999999) or Words (e.g., seven million...)

Result (Tap to Copy):

Copied!

*Supports positive whole numbers up to 999,999,999.

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