  We present a systematic search for wide-separation (Einstein radius >1.5"),
galaxy-scale strong lenses in the 30 000 sq.deg of the Pan-STARRS 3pi survey on
the Northern sky. With long time delays of a few days to weeks, such systems
are particularly well suited for catching strongly lensed supernovae with
spatially-resolved multiple images and open new perspectives on early-phase
supernova spectroscopy and cosmography. We produce a set of realistic
simulations by painting lensed COSMOS sources on Pan-STARRS image cutouts of
lens luminous red galaxies with known redshift and velocity dispersion from
SDSS. First of all, we compute the photometry of mock lenses in gri bands and
apply a simple catalog-level neural network to identify a sample of 1050207
galaxies with similar colors and magnitudes as the mocks. Secondly, we train a
convolutional neural network (CNN) on Pan-STARRS gri image cutouts to classify
this sample and obtain sets of 105760 and 12382 lens candidates with scores
pCNN>0.5 and >0.9, respectively. Extensive tests show that CNN performances
rely heavily on the design of lens simulations and choice of negative examples
for training, but little on the network architecture. Finally, we visually
inspect all galaxies with pCNN>0.9 to assemble a final set of 330 high-quality
newly-discovered lens candidates while recovering 23 published systems. For a
subset, SDSS spectroscopy on the lens central regions proves our method
correctly identifies lens LRGs at z~0.1-0.7. Five spectra also show robust
signatures of high-redshift background sources and Pan-STARRS imaging confirms
one of them as a quadruply-imaged red source at z_s = 1.185 strongly lensed by
a foreground LRG at z_d = 0.3155. In the future, we expect that the efficient
and automated two-step classification method presented in this paper will be
applicable to the deeper gri stacks from the LSST with minor adjustments.
