from any blockcipher (for example as Threefish as mentioned by Gro-Tsen) you can build various other primitives. This is heavily related to their mode of operation. You can find basic pointers in wikipedia's article on block ciphers.But usually one uses dedicated algorithms for different problems like encryption, hashes, etc..
However there are other much more general approaches, for example many primitives can be seen as instances of sponge constructions. But it is hard to guess what you are looking for.
Also 'cryptographic primitive' is more an idea rather than a fixed notion. It is distinguishes 'cryptographic algorithms' from 'cryptographic schemes'. There is a beautiful paper from U.Maurer: Constructive cryptography about 'pasting' primitives.
All this said, it seems to be a question for crypto.stackexchange. Also you should provide more background in what (and why) your are interested.