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 alogrithm, does not get back to the same rythm 4 -> 2 -> 1 -> 4
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 your 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 succesfully reached 1.
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 which are tilted slightly to the left and where odd numbers are tilted slightly to the right.
Since Juli 2014 around 4700 computer 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.