Technically, it is the giant, because it cannot be spawned in creative or survival.
You require a 3rd party program to spawn the giant.
The rarest mob that is spawned, is the enderdragon.
There is only 1 in The End.
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there are no horses
its not a rock but it is the rarest without a mod is emerald ore
Go to minecraft wiki and do a search for "mob grinder" and it gives you a tutorial of how to do it.
Emerald I think
You cant find a giant mob in vannilla minecraft but you can sumon him using a command or a spawner.