I found in Wikipedia that Somebody Else™ checked that there are no counterexamples up until 2^68.

So my attempt to find a counterexample is to start at (2^68)+1, and perform the 3x+1 or halving until I get to a number that's lower than the one I'm testing - then I know it's not a counterexample.

Since even numbers start by halving (ie, getting lower), I only test odd numbers.

295147905503560000001 and counting. No counter-examples found yet.