Mammillaria gracilis Pfeiff.

Snowcap Cactus

Freely clustering, body elongate, up to 13 cm high, 1-2(-4.5) cm wide, without milky sap. Tubercles prominent. Axils slightly woolly. Central spines 3-5, to 10 mm long, brownish. Radial spines 12-14, 3-8 mm long, white. Flowers white to about 1.2 cm wide. Fruit red. [M. fragilis Salm.-Dyck.]

EC Mexico

Sometimes sold under the name Frosty.

Source: Thompson, A, ; Forbes, S.; Spencer, R. (1997). Cactaceae. In: Spencer, R.. Horticultural Flora of South-eastern Australia. Volume 2. Flowering plants. Dicotyledons. Part 1. The identification of garden and cultivated plants. University of New South Wales Press.

kingdom Plantae
phylum   Tracheophyta
class    Magnoliopsida
superorder     Caryophyllanae
order      Caryophyllales
family       Cactaceae
genus        Mammillaria Haw.