  Let $\Psi$ be a system of linear forms with finite complexity. In their
seminal paper, Green and Tao showed the following prime number theorem for
values of the system $\Psi$: $$\sum_{x\in [-N,N]^d} \prod_{i=1}^t
\mathbf{1}_{\mathcal{P}}(\psi_i(x)) \sim \frac{(2N)^d}{(\log N)^t} \prod_{p}
\beta_p,$$
  where $\beta_p$ are the corresponding local densities. In this paper, we
demonstrate limits to equidistribution of these primes on small scales; we show
the analog to Maier's result on primes in short intervals. In particular, we
show that for all $\lambda > 1$, there exist $\delta_\lambda^\pm > 0$ such that
for $N$ sufficiently large, there exist boxes $B^\pm\subset [-N, N]^d$ of
sidelengths at least
  $(\log N)^\lambda$ such that
  $$\sum_{x\in B^+} \prod_{i=1}^t \mathbf{1}_{\mathcal{P}}(\psi_i(x)) >
(1+\delta^+)
  \frac{\mathrm{vol}(B^+)}{(\log N)^t} \prod_{p}\beta_p,$$
  $$\sum_{x\in B^-} \prod_{i=1}^t \mathbf{1}_{\mathcal{P}}(\psi_i(x)) <
(1-\delta^-)
  \frac{\mathrm{vol}(B^-)}{(\log N)^t} \prod_{p}\beta_p.$$
