Are results that are derived simply by using more computational power publishable? Let's say Alice has written a paper that attacks a well-known problem in a clever new way. Her paper ends with "these methods work up to N = 10; for larger N, the calculations are prohibitively expensive".

Bob reads the paper and successfully duplicates Alice's results, but where Alice only had access to a 4-core desktop, Bob has a 4000-core supercomputer. Therefore he can calculate what Alice found prohibitively expensive, and get results up to N = 20.

Are Bob's results publishable? He didn't actually do anything special, he just had more computational power. On the other hand, the results are definitely new, and interesting (for whatever reason N = 20 is the point where interesting effects are predicted).

If they are publishable, what would Bob actually write in such a paper? Everything sans the result could effectively be communicated in one sentence ("Read Alice's paper"). If they are not publishable, how is Bob to communicate his results to the wider world?

I suspect something like this has happened in the past, in which case I'd appreciate a link to such a paper.
(I switched the order of a couple of your questions to give the answer a more logical flow.)


  On the other hand, the results are definitely new, and interesting (for whatever reason N = 20 is the point where interesting effects are predicted).


If the results are new, and interesting, then they are by definition publishable. The key point is they add something meaningful to the sum total of human knowledge. That’s certainly a sufficient criterion for publishability (in an idealized sense it should be necessary as well, but I fear it isn’t - plenty of things get published that don’t really meet this condition).


  Are Bob's results publishable? He didn't actually do anything special, he just had more computational power. 


The concept of “doing something special” is both mostly meaningless and (to the small extent that it has any meaning) completely irrelevant to the question of publishability. Plenty of authors of excellent papers “didn’t do anything special” - they just had more patience and were willing to work a bit harder, or in many cases just got a little bit luckier, than their peers, and ended up discovering something significant. Publication is not a prize that’s given for “doing something special”, it’s simply the scientific community putting a stamp of approval on a discovery that it is correct, new, and worth paying attention to.

By the way, one can even say that a researcher Bob who works harder than his peer Alice is pretty much the exact scenario you are describing of someone “having more computational power”. In this case the computational power is of the human sort, but I don’t see why that should change the calculation.

Edit: another thought is that Bob actually did “do something special”. It’s not just that he had more computational power, but he had the foresight and intuition to realize that it would be worthwhile to apply that computational power to Alice’s particular problem rather than spend his time and resources doing any number of other things. So although it’s not really that important as I said above, even by your own criterion I think there is more merit to the achievement than your description makes it sound.


  If they are publishable, what would Bob actually write in such a paper? Everything sans the result could effectively be communicated in one sentence ("Read Alice's paper"). 


Bob would simply write what he did and what the results were, and what makes them interesting. If it can really be described in one sentence I’d argue that it likely wasn’t such an interesting result after all. But on the off-chance that it was indeed interesting, then it would make for a great one-sentence paper. There isn’t any rule that papers have to be longer than one sentence.