If you like this stuff, have a look at Healpix: http://healpix.sourceforge.net/
It splits sphere into pixels each with separate number. It is sort of fast hashing for spherical purposes in astronomy. It does not require trigonometric operations and is very fast.
There is another free library to do that, among other things, by Google. It's not well known, but it was used all over the place internally (at least by the geo team).
The key difference with geohash is that it uses a Hilbert curve instead of a z-curve and it projects the world in a cube instead of using directly cartesian coordinates.
When the prefix (or infix) doesn't match for something that is close it looks like the prefixes are simply inverted. So 10000 and 01111 are obviously close. I haven't verified.