For the longest time I was under the impression that PR contains NEXP. Try as I might, I am unable to recall where I picked up this notion. I've looked recently, but I have not been able to find anything about what is known about their relationship.
All that I can currently conclude about them is that it's almost certainly not the case that PR = NEXP, as there are known NEXP-complete problems, while the notion of completeness for PR is problematic.
What is known about the relationship between PR and NEXP?