Hi, and welcome to the Forum.
I am having difficulty with this plant, as I don't recognise a white spined plant like this, with such a strong and thick dark upwards pointing central spine.
I wondered about andersoniana, but the radial spines are not right; then I wondered about a form of gracilis, with its chalky white spines, and of which there are many hybrids and cultivars. But I am not at all sure. Can you tell us the size of the plant, and if it has flowered?
I have also wondered if it is an Escobaria?
I'll have a look through my books to see I can find anything that looks like it.