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It's easy to write a 5-line Python program to check this up to, say, x = a trillion (or much further). But proving it turns out to be something else entirely! Lots of mathematicians have worked on this, and failed to solve it.
It's a lovely problem, in part because you can goof around with it from first principles, & learn fun stuff. I did a lot of this when I was 18, 19 or so, & even today occasionally pull the problem out to relax. But people have also brought quite sophisticated mathematics...
... to bear on the problem. Much has been learned, but the problem remains unsolved!
More detail in the Wikipedia article: https://en.wikipedia.org/wiki/Collatz_conjecture … And, via @geomblog, the news that Terry Tao has recently made some very interesting progress:https://terrytao.wordpress.com/2019/09/10/almost-all-collatz-orbits-attain-almost-bounded-values/ …
Sigh. @nathanju34 points out that in case (2) above I should have written "odd", not even, of course. My kingdom for an edit button.https://twitter.com/michael_nielsen/status/1172916056496558080 …
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