Identification: Cactus ID needed if possible

Hi there, if possible, I am trying to figure out which species these following cacti are.
My cactus and succulent book has failed me. They may be so common, that they don't show up in my book at all, except for the white hairy one, with spines.
Thanks for any tips

I forgot to mention, that the first 2 shots, are all in 4" pots, and are of a nice
size. baseball to softball size.

Thanks again for any identifications.
Ken

 

Think the white hairy one is Oreocereus Trolli or 'old man's cactus', only because i just got one and it looks exactly like yours. It's one of my newest additions and he is cute and fluffy and I love him:)

Not sure about the others sorry:(

 

The two in the middle look like Echinopsis of some sort. Can't help with number 1 though.

 

1. Notocactus crassigibbus /syn. Parodia crassigibba

 

I think the left one in the middle photo maybe be a Gymnocalcium? Cactus i.d. has been giving me headaches lately and, for some reason, every time I start I always find something else that drags me away from it :}

 

Two in the the middle, the left one, Coryphantha elephantidens? Right one,
Coryphantha sulcolanata?

 

Unfortunately I'm also not sure what are they, but I don't think they are Coryphanthas... the left one looks more like a Gymnocalycium (multiflorum)... (right one: Mammillaria sp. ?)

 

Thanks to all who were able to answer. I now have a few names I can search on the internet from your notes, which I was hoping would happen,and hope they flower for more postive id's.
Thanks again for checking!
Ken in Uxbridge

Hi there.......could the first picture be Gymnocalycium denudatum? Or the "spider cactus"
It does look like mine, when I compare.