I worked on the Collatz conjecture extensively for fun and practise about a year ago (I'm a CS student, not mathematician). Today, I was browsing the Project Euler webpage, which has a question related to the conjecture (longest Collatz sequence). This reminded me of my earlier work, so I went to Wikipedia to see if there's any big updates. I found this claim
The longest progression for any initial starting number less than 100 million is 63,728,127, which has 949 steps. For starting numbers less than 1 billion it is 670,617,279, with 986 steps, and for numbers less than 10 billion it is 9,780,657,630, with 1132 steps.
Now, do I get this correctly: there is no known way to pick a starting number $N$, so that the progression will last at least $K$ steps? Or, at least I don't see the point of the statement otherwise. I know how this can be done (and can prove that it works). It does not prove the conjecture either true/false, since it is only a lower bound for the number of steps. Anyway, I could publish the result if you think it's worth that? When I was previously working on the problem, I thought it was not.