That math doesn't seem to check out. Say with base-2 log and a 27 factor difference, for 1000 it would be 1000^2 = 1,000,000 vs 27 * 1000 x log 1000 = 270,000. I wouldn't call n=1000 an extreme case for most problems. Just because practical counterexamples exist, don't think that it applies to your problem unless demonstratably so, an then still worry about N being larger than originally designed for.