If you know the public key (not the address) and the first ~ 180 bits of the private key, it is possible to retrieve the other 70 / 80 bits using smarter ways than brute force attack.
Yes, I realize that finding the last bits of the private key would be much easier.
Unfortunately... I know only what I have shown: full addres, and private key with some randomly missing characters.
The address is not the public key. It's a hash of a hash of the public key plus a bit of error correction.
If there has been an outgoing transaction from the address in question one is able to extract the public key from the raw transaction like so:
https://bitcoin.stackexchange.com/questions/32305/how-does-the-ecdsa-verification-algorithm-work-during-transaction/32308#32308If there never has been an outgoing transaction from the address in question it's pretty much impossible to get even just the public key.