M. heyderi? E. vivipara?

Hi all,
First post here and hoping you can help ID these two wee beauties. From my own research I believe the one with the pink flowers to be Escobaria vivipara, but am unsure on the other. It was sold as simply a Mammilaria but I was wondering if it was possibly a heyderi or spinossima? Any insight you can give would be greatly appreciated!

1, Mammillaria backebergiana ?
2, Mammillaria zeilmanniana
Üdvözlettel Józsi

Thank you so much! I thought I was close with E. vivipara but you’re absolutely right, unmistakably zeilmanniana. I agree that the first Mammilaria looks a lot like backbergiana but may have to wait until it grows to know for sure. I will happily label it backebergiana for now!