Could be a M. mystax or a M. magnimamma. My best guesses. Hard to tell what size it is. Bob

Nice one Fred --- I think you tagged it...Thanks!....and I found a pretty cool site as a result of your answer. Copy and paste this [Doña Púa] into Google and the first site that comes up has some excellent photos/ids of some cactus: Doña Púa Lots of you vets probably know this one, but it was new to my eyes :-) The Mammillaria you id'ed is on the Doña Púa site too... Now I need to go back to that site and see if there were any succ pics/ids Thanks again Fred

Thank you all. And based on Harry's plant, I don't think I will be dividing it. Maybe just repotting it.

Someone else suggested to me that it was Dog Tail (Selenicereus testudo). I think the spines/fuzz are really similar to that, though Dog Tail seems to have more "ridges" -- all of the stalks on mine only have 3, and a few are just flat, while Dog Tail seems to have at least 4 (that's also why I'm not sure it's Acanthocereus tetragonus, because even the young ones seem to be bigger, with more ridges with prominent white dots). Maybe it's because this one's young, but I feel like the oldest growth would be starting to look more like testudo or tetragonus by now if it was one of those... but maybe not! I didn't think it was Acanthorhipsalis/Pfeiffera because of this one's fuzziness around the spines... and it seems like the Pfeiffera is mostly flat, not deeply ridged like most of these. But I'd be excited to see those flowers if that's what this really is! But it does seem to look like some kind of Selenicereus -- a lot of that group seem to have long spindly stalks like this. I want to repot, but if it's going to be an epiphyte like that I might put it in a hanging basket rather than a little table pot. Polypompholyx - will all the nubs that fall of the thimble cactus be rooted as the are? I can't even tell where there's a connection point that a root would grow out of! They're all just little pebbles and grubs. :)