Echinocereus purpureus, although the recently out-of-print The Cactus Family (Anderson) says its more recently changed to the corrected E. reichenbachii ssp. reichenbachii, but we also grow E. reichenbachii and then there’s E. baileyi which they say is more properly known as E. reichenbachii ssp. baileyi and E. armatus which Anderson insists is really E. reichenbachii ssp. armatus, so that’s all just too confusing and I prefer to go with the E. purpureus for this one.
Now that’s what Botany and Botanical Latin and the whole Horticulture trade is all about – getting the proper names right.
(The Merry Widow Cactus common name above is real, although Anderson also has listed the less distinctive Purple Candle Cactus.)