producing GnuPG keys as proof of work

[Robert J. Hansen]

> Would it be feasible to use gpg in batch mode to generate numerous keys,
> selecting for a particular key ID, or perhaps a longer part of the
> fingerprint?

Depends.  Expert users, sure; new users, or people who aren't that
interested in GnuPG but just want to get access to a website, not so much.

> I imagine that websites could provide random alphanumeric strings to new
> users, and require them to generate functional GnuPG keys (with normal
> key length etc) with fingerprints that begin with the specified strings.
> Having accomplished that, new users could edit their key, and specify an
> account name and email address.

I have to ask -- why?  What particular use case is this?  Why use GnuPG
as a proof-of-work as opposed to giving someone six bytes and saying,
"find me a SHA256 hash that starts with this, and provide me with it"?