  We report the discovery of PSR~J2251$-$3711, a radio pulsar with a spin
period of 12.1 seconds, the second longest currently known. Its timing
parameters imply a characteristic age of 15 Myr, a surface magnetic field of
$1.3 \times 10^{13}$~G and a spin-down luminosity of $2.9 \times
10^{29}~\mathrm{erg~s}^{-1}$. Its dispersion measure of
12.12(1)~$\mathrm{pc}~\mathrm{cm}^{-3}$ leads to distance estimates of 0.5 and
1.3 kpc according to the NE2001 and YMW16 Galactic free electron density
models, respectively. Some of its single pulses show an uninterrupted 180
degree sweep of the phase-resolved polarization position angle, with an S-shape
reminiscent of the rotating vector model prediction. However, the fact that
this sweep occurs at different phases from one pulse to another is remarkable
and without straightforward explanation. Although PSR~J2251$-$3711 lies in the
region of the $P-\dot{P}$ parameter space occupied by the X-ray Isolated
Neutron Stars (XINS), there is no evidence for an X-ray counterpart in our
Swift XRT observation; this places a 99\%-confidence upper bound on its
unabsorbed bolometric thermal luminosity of $1.1 \times 10^{31}~(d /
1~\mathrm{kpc})^2~\mathrm{erg/s}$ for an assumed temperature of 85 eV, where
$d$ is the distance to the pulsar. Further observations are needed to determine
whether it is a rotation-powered pulsar with a true age of at least several
Myr, or a much younger object such as an XINS or a recently cooled magnetar.
Extreme specimens like PSR J2251$-$3711 help bridge populations in the
so-called neutron star zoo in an attempt to understand their origins and
evolution.
