Collatz Conjecture
What is the Collatz Conjecture?
Take any positive integer greater than 1 and apply two simple rules:
- If it's even, divide it by 2
- If it's odd, multiply by 3 and add 1
Repeat this process. The conjecture states that no matter what number you start with, you will always eventually reach 1. Simple to state, yet no mathematician has ever proven - or disproven - it. Legendary mathematician Paul Erdos said of it: "Mathematics is not yet ready for such problems."
Try it yourself
Spiral
Collatz Conjecture
Even? Divide by 2. Odd? Multiply by 3 and add 1. Always reaches 1... apparently.
Try 27 (111 steps) or 871 (178 steps)
Some fun starting points
| Number | Steps to reach 1 | Peak value |
|---|---|---|
| 6 | 8 | 16 |
| 27 | 111 | 9,232 |
| 871 | 178 | 190,996 |
| 6,171 | 261 | 975,400 |
The number 27 is famous for being deceptively small yet taking 111 steps and shooting up to 9,232 before finally collapsing back down to 1 - a great one to try first.