What is known about the relationship between PR and NEXP? 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?
Transforming the comments above into an answer: 

NEXP is strictly contained in PR. Indeed define the class ELEMENTARY as 
$$\mathsf{ELEMENTARY}=\text{DTIME}(2^n)\cup \text{DTIME}(2^{2^n}) \cup \text{DTIME}(2^{2^{2n}}) \cup ...$$

It can be shown that ELEMENTARY is strictly contained in PR. Since $\mathsf{NEXP}\subseteq \mathsf{ELEMENTARY}$ we have that $\mathsf{NEXP}$ is strictly contained in $PR$. 

As pointed out by Huck Bennett above, the fact that $\mathsf{NEXP}\subseteq \mathsf{ELEMENTARY}$
is a consequence from the fact that 

$$\mathsf{NEXP} = \text{NTIME}(2^{\text{poly}(n)}) \subseteq \text{DTIME}(2^{2^{2^n}}) \subsetneq \mathsf{ELEMENTARY}$$