any idea what this big mammi is?

It looks like it has had pink flowers, and with bristles and hairs in the axils, I am thinking it might be an interesting form of Mammillaria mystax. My concern about that diagnosis is that I have never seen such a white form of mystax, the spines, centrals especially are usually darker. It is a very variable species though...... Did you grow it from seed?

Looks like a pretty classic geminispina with long spines to me ?!?

M. geminispina has many radial spines, 16-20 approx. This plant has much fewer, maybe 5 radials and the big central. I know spine counting is only an approximate guide, but that's a bit too few, I think.

thank you both Chris43 and mmartic,
The plant is not mine, it is in a pot in the garden of a GuestHouse in Galaxidi in southern Greece. It grows in an open space with lots of sun. The owners gave me 2 pups from the base. It has a stem of more than 10cm diameter, I don't know if this passes with geminispina

Chris43 wrote:

M. geminispina has many radial spines, 16-20 approx. This plant has much fewer, maybe 5 radials and the big central. I know spine counting is only an approximate guide, but that's a bit too few, I think.

A bit too few
Pitty, overall look is geminispinical
There are also similarities with some karwinskiana forms, but pink flowers...
Interesting plant anyway!!!

I don't think it has anything to do with geminispina, to me it looks more nejapensis/karwinskiana related. The ring of flowers is also not geminispina-like, because geminispina usually flowers very sparingly. What the flower colour has been is difficult to say, the colour of dried flower remains is not a good indication in my opinion.

Wolter ten Hoeve.

No not geminispina. I agree with wolter, more akin to karwinskiana. Could possibly be karwinskiana subsp. beiselii.

Thanks delandmo, a thick spined form of karwinskiana subsp. beiselii looks like the best guess,
it branches from the base though, does this happen with any karwinskiana?

Hi xocolati, karwinskiana will branch from the sides and/or divide dichotomously.