Don't ask why, just is it possible to install old mysql 3.23 on new CentOS 6.4 i386 or x64 version (same to me)?
Searched on this one for a while. Not finding anything older than 4.1.
Your only option will be to find the Linux Generic Architecture Independent builds which are designed to run self contained from a directory. We've used these in the past and they work well.
Continuing the search I'm not finding it as available. I searched Google using this: