To paraphrase a recent blog post (possibly by rjlipton?), one good reason to avoid a specific concrete example is that the answer to P=NP or P!=NP isn't quite a

To paraphrase a recent blog post (possibly by rjlipton?), one good reason to avoid a specific concrete example is that the answer to P=NP or P!=NP isn't quite as important as the specific time complexities involved in solving NP problems - for most practical purposes 1.000000001^n would be much more favourable than n^1000000000.