  We have newly developed a Parallelized Particle-Particle Particle-tree code
for Planet formation, PENTACLE, which is a parallelized hybrid $N$-body
integrator executed on a CPU-based (super)computer. PENTACLE uses a 4th-order
Hermite algorithm to calculate gravitational interactions between particles
within a cutoff radius and a Barnes-Hut tree method for gravity from particles
beyond. It also implements an open-source library designed for full automatic
parallelization of particle simulations, FDPS (Framework for Developing
Particle Simulator) to parallelize a Barnes-Hut tree algorithm for a
memory-distributed supercomputer. These allow us to handle $1-10$ million
particles in a high-resolution $N$-body simulation on CPU clusters for
collisional dynamics, including physical collisions in a planetesimal disc. In
this paper, we show the performance and the accuracy of PENTACLE in terms of
$\tilde{R}_{\rm cut}$ and a time-step $\Delta t$. It turns out that the
accuracy of a hybrid $N$-body simulation is controlled through $\Delta t /
\tilde{R}_{\rm cut}$ and $\Delta t / \tilde{R}_{\rm cut} \sim 0.1$ is necessary
to simulate accurately accretion process of a planet for $\geq 10^6$ years. For
all those who interested in large-scale particle simulations, PENTACLE
customized for planet formation will be freely available from
https://github.com/PENTACLE-Team/PENTACLE under the MIT lisence.
