Is there a pair correlation function for primes?

Question

Montgomery's pair correlation function for the non-trivial zeros of the Riemann $\zeta(s)$ function is defined via the term $$1- \left( \frac {\sin(\pi u)}{\pi u} \right)^2$$

Does anybody know if there exists a pair correlation function for the sequence of the primes as well?

Thanks in advance

Answer 1

Indeed found the answer in a cascade over here this is back to the difference between a Gaussian unitary ensemable and a Poisson ensemble. Exciting although simple: No random matrices for primes, sure.