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 

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