Ever since I started studying asteroids in grad school, I've been saving a daily copy of the Minor Planet Center's Orbit Database, "MPCORB." To save hard drive space, I store them in a subversion repository that only saves the changes since the previous version. (That's why you may see references to "revision numbers" alongside dates on my website.) This archive makes it possible to answer questions like: What did we know about Asteroid X on Date Y? How many new asteroids in Category Z are discovered every year?
But there was one question I couldn't answer with this archive, because it only reaches back to mid-2006. That question: How many asteroids have been "numbered" but not "named" for at least the last 10 years? Perhaps a bit more explanation is in order. When an asteroid is first discovered, it's given a provisional designation based on the date it was first reported, e.g., "2005 RN43". Some become lost at this point, because insufficient observations are made of the object, and our certainty in predicting its position degrades to the point where the object essentially has to be rediscovered all over again. But when the object is properly tracked and its position is well-known for the coming decade or longer, it gets a number, e.g., "(145452) 2005 RN43". At this point, the object is eligible for naming, but that privilege is reserved for the discoverer for the first 10 years after numbering.
So back to the question: How many asteroids have been "numbered" but not "named" for at least the last 10 years? These would be eligible to be given proper names, but the privilege of the discoverers to do so would have expired. Anyone could suggest names for these objects, although it's up to the Committee on Small Body Nomenclature of the International Astronomical Union to approve or deny them.
As I said, my MPCORB archives don't go back a decade, but I recently stumbled on a resource that could help me answer this question. The Wayback Machine (https://archive.org) contains old archived versions of various webpages, including about 28 old versions of MPCORB from 2001-2007. One of these was from 2004 October 10th, about 10 years and 2 months ago.
So, how many asteroids that were numbered by Oct 2004 still lack a proper name today? How many nameless space-rocks are just waiting for a clever suggestion from us, the hoi-paloi?
Over 73,400!
And I suspect that number is growing, although I haven't done the necessary analysis to prove it.