On a fresh install of PB on a Pi1B, it seems that pacman is broken and cannot downoad anything.
sudo pacman -Syu
:: Synchronizing package databases...
error: failed retrieving file 'core.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update core (download library error)
error: failed retrieving file 'extra.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update extra (download library error)
error: failed retrieving file 'community.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update community (download library error)
error: failed retrieving file 'alarm.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update alarm (download library error)
error: failed retrieving file 'aur.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update aur (download library error)
error: failed to synchronize any databases
error: failed to init transaction (download library error)
sudo pacman -Syu
:: Synchronizing package databases...
error: failed retrieving file 'core.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update core (download library error)
error: failed retrieving file 'extra.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update extra (download library error)
error: failed retrieving file 'community.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update community (download library error)
error: failed retrieving file 'alarm.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update alarm (download library error)
error: failed retrieving file 'aur.db' from mirrors.kernel.org : Could not resolve host: mirrors.kernel.org
error: failed to update aur (download library error)
error: failed to synchronize any databases
error: failed to init transaction (download library error)