I don't normally like to jump on when there's already a pile of other posters, but in this case I think everyone else has overlooked a fundamental misunderstanding:
That asked, the chances of the mutations required between human and primate, occurring in the right gene and often enough in the population to change the genome of the entire species, are next to naught.
A specific mutation doesn't need to happen often to become characteristic of a species. It only needs to happen once. It can then spread throughout the population by inheritance.
If it's an advantageous mutation, then it's likely to spread much more quickly than if not. When we talk about an advantageous mutation, all we really mean is one whose possessors are liable to leave more children in the next generation than those without. So each successive generation a higher proportion of the population will possess this mutated form of the gene; even though the mutation only happened once.
That's what natural selection is.
Edited by caffeine, : No reason given.