Mammillaria paintneri

I googled it and it seems normal for the flowers to be like this. The only photo of fully open flowers carried an interesting explanation - they grafted onto various rootstock and the best (as in most open flowers) result came from grafting it onto Opuntia compressa.

(the site was Cactus-art biz)

That's interesting to know.
I often look at the Cactus-art site. I've been able to identify several unnamed cacti from it, and it gives interesting information.

I've been there a few times recently too. It's a good source of info for a newbie.

And for everyone else too :)