Collatz Conjecture

The Collatz conjecture is a to this day still not proven mathematical conjecture from Lothar Collatz. The Collatz conjecture tries to find a number n ∈ N that, after processing the algorithm, does not get back to the same rhythm 4 → 2 → 1 → 4.

How is this algorithm defined?

Get your arbitrary value n. If it's even divide by 2 and if it's odd multiply by three and add one. So for example lets take n = 10: even → 10 / 2 = 5. Then continue until you've reached 1: odd → 5 * 3 + 1 = 16 even → 16 / 2 = 8 even → 8 / 2 = 4 even → 4 / 2 = 2 even → 2 / 2 = 1 and we've successfully reached 1.

Note

By the time that you've read this small paragraph, your browser executed the "collatzConjecture.js" file and checked the Collatz conjecture for the first 10k numbers. The conjecture can also be visualized in an image where even numbers are displayed as a small line segment tilted slightly to the left and where odd numbers are tilted slightly to the right. You can see the resulting visualization below.

Fact

Since July 2014 around 4700 computers world wide try to find a natural number n that does not follow the described algorithm and would therefore prove the Collatz conjecture ( ref). Numbers above 2.361.183.346.958.000.000.001 are currently observed.