Don't run your finger lengthwise down the blade edge - ever. By the time you realize you're being cut, it is too late. I've known a couple guys who tested their knife's sharpness that way once, and cut themselves badly. (surprisingly, they were intelligent enough not to test the sharpness that way a second time.)
Go across the blade, if you must.
For a true test of sharpness, lay your off hand flat on a table. Place the blade edge on a fingernail. Then, keeping the knife vertical, with just the weight of the blade on your finger/thumb nail, slowly and smoothly angle your finger or thumb nail. (keep fingertips on the table and slide hand forward, is one way to do it) You don't want the blade to slip off until at least a 60 degree angle.
As others have stated, a "razor's edge" isn't necessary, and truth to tell, isn't practical for "real life" usage either. A "razor's edge" is actually quite delicate.