What I want to know is if an asteroid about 15 KM in diameter and roughly double that in length, spinning at a significant speed, could go undiscovered until a crew of an asteroid mining ship happened upon it, out in the belt (specifically the Mars/Jupiter belt, not the Kuiper belt).
A little bit of extra information that may or may not affect this likelihood - man at the time of this story does have a significant population in space, with Earth-orbital colonies, a few lunar and Martian colonies, and a significant presence out there in the belt. The belt is so huge and vast and so full of objects though, could an asteroid like this, that's not exceptionally bright/reflective, go unnoticed until stumbled upon?
[EDIT] The spin would be maintained artificially. Technology is present the humans won't fully comprehend, and thus I don't have to fully reconcile. Presumably, this would also prevent it from going into a tumble.
[EDIT #2 - Shame on me for needing to revise this twice!] BeauM raised a point I should've thought of, and that's specifying the level of advancement/time period for humanity in this case. I place this around 175 or so years into the future, which I see as an awful optimistically short period of time to be where they are with space colonization really. But it's possible. They've got nuclear propulsion working well enough to reach Mars in a couple months when it's at its closest. They've got decent laser drills to carve asteroids up, and they've got decent centrifugal "gravity" on ships and orbital stations to make space habitation comfortable. But they've not achieved any magical leaps in technology. Telescopes aren't all that much more powerful than our newest exoplanet hunting setups, they merely have the opportunity to put more of them in more advantageous places. Really the only fantastic leap, which made space so much more accessible, was the construction of decent magnetic launchers to escape Earth affordably and mostly safely.