# Metaculus

## Question

### Metaculus Help: Spread the word

If you like Metaculus, tell your friends! Share this question via Facebook, Twitter, or Reddit.

# Is the Collatz Conjecture true?

A sister question asks when the Collatz Conjecture will be resolved - here we ask which way it will turn out.

Again, let's say that the Collatz Program in pseudocode is:

```
collatz(n) =
if (n is 1) return 1
else if (n is even) return collatz(n/2)
else return collatz(3n + 1)
```

where n is a positive integer.

The Conjecture is that for all integer inputs the Collatz Program halts (and returns 1).

For any particular execution of the Collatz program, there are three possible outcomes:

1) It moves up and down through input arguments of different sizes, until it encounters a power of 2, and then cascades down to 1, and halts.

2) It moves up and down through numbers of different sizes until it repeats a number. From that point onward it will repeat a cycle, and never halt.

3) It moves up and down through numbers of different sizes, but keeps expanding its frontier of numerical size, without ever repeating an input or encountering a power of 2. In this case, it will never halt.

Per Wikipedia, Jeffrey Lagarias in 2010 claimed that based only on known information about this problem, "this is an extraordinarily difficult problem, completely out of reach of present day mathematics."

*This question will resolve positively if there is a positive proof of the Conjecture (i.e. that the Collatz Program halts for all integer inputs) in a major Mathematics journal before June 21, 2520. It will resolve negatively if there is a publication of a disconfirmation in a major mathematics journal before that time.*

If the Conjecture has neither been proven nor disproven before that time, it will resolve as ambiguous.

Other questions on the Collatz Conjecture:

### {{qctrl.predictionString()}}

### Metaculus help: Predicting

Predictions are the heart of Metaculus. Predicting is how you contribute to the wisdom of the crowd, and how you earn points and build up your personal Metaculus track record.

The basics of predicting are very simple: move the slider to best match the likelihood of the outcome, and click predict. You can predict as often as you want, and you're encouraged to change your mind when new information becomes available.

The displayed score is split into *current points* and *total points*. Current points show how much your prediction is worth *now*, whereas total points show the combined worth of all of your predictions over the lifetime of the question. The scoring details are available on the FAQ.

Note: this question resolved before its original close time. All of your predictions came after the resolution, so you did not gain (or lose) any points for it.

Note: this question resolved before its original close time. You earned points up until the question resolution, but not afterwards.

This question is not yet open for predictions.

#### Thanks for predicting!

Your prediction has been recorded *anonymously*.

Want to track your predictions, earn points, and hone your forecasting skills? Create an account today!

##### Track your predictions

##### Continue exploring the site

Community Stats

### Metaculus help: Community Stats

Use the community stats to get a better sense of the community consensus (or lack thereof) for this question. Sometimes people have wildly different ideas about the likely outcomes, and sometimes people are in close agreement. There are even times when the community seems very certain of uncertainty, like when everyone agrees that event is only 50% likely to happen.

When you make a prediction, check the community stats to see where you land. If your prediction is an outlier, might there be something you're overlooking that others have seen? Or do you have special insight that others are lacking? Either way, it might be a good idea to join the discussion in the comments.

### Embed this question

You can use the below code snippet to embed this question on your own webpage. Feel free to change the height and width to suit your needs.