If you read the Wikipedia page carefully and go to geohash.org, you’ll see that this isn’t entirely accurate. There are many ways to explore the algorithm to find nearby places indeed, but computing how close two different Geohashes really are by merely comparing the string prefixes “blindly” (IOW, without taking the algorithm used in consideration) wasn’t one of the goals, even because it’s an impossible one. I’ll try to make that more clear in the page to prevent misunderstandings.

Suppose, for instance, that an algorithm established that places which are N kilometers apart must necessarily have the same first character. As a corollary, all places on earth would have to start with the same character. Picking lexically closeby characters to represent the boundary doesn’t work either, because the earth is round.

The often similar prefixes come, in fact, as a bonus of one of the goals of the algorithm, which was allowing for gradual degradation of the position by reducing the geocode size.