mammillaria bachmannii

referred to mammillaria sempervivi....
referred to mammillaria orcutti...

...

Has you seem to know, the name bachmanni is ' attributable to sempervivi, athough plants in cultivation under this name have been referable to orcutii ' Pilbeam, page 319.
To me this plant looks like neither of these 2 speices. If I was going to put a name to this it would be some thing like formosa pseudocrucigera.

so, you think that this is not a bachmannii?

The name game is a bit of a minefield that is best left alone. I do not accept bachmannii as a correctly applied name and would not use it in my collection.
That does not mean to say that you cannot use it for a plant in your collection.
It does not look like orcuttii or sempervivi to me, but it does look like pesudocrucigera.

clear as usual.
thank you.