Hi Arthur,
Interesting couple of white flowered Mamms! I think Maurillio is right about the other one being rekoi aureispina, but this one I don't have an immediate answer. The shape of the plant and the spines look as though it might be M. spinosissima, but I'm not aware of a white flowered clone. There are some related species that do have white flowered forms, such as M. duoformis but this one is more of a mystery.
Sorry not to help more, hopefully some other members might know it.
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Chris43, moderator