nice looking Mammillaria grahamii. I thot this was interesting: (also known as mammillaria microcarpa) is the most common fishhook cactus in Arizona, and the only one found in the Phoenix area. According to the American Southwest Desert Flora website Common name: Graham's nipple cactus, Arizona fishhook cactus.
https://www.americansouthwest.net/plant ... hamii.html
According to Southwest Desert Flora also Called: Arizona Fishhook Cactus, Graham Pincushion Cactus (Spanish: Cabeza de Viejo, Choyita) http://southwestdesertflora.com/Website ... actus.html

FYI: It becomes more visible in spring and summer when the pretty pink flowers open, arranged in a neat circle a little way below the apex. These are followed by long, thin, red fruits.