The PRobe far-Infrared Mission for Astrophysics (PRIMA) concept aims to perform mapping with spectral coverage and sensitivities inaccessible to previous FIR space telescopes. PRIMA's imaging instrument, PRIMAger, provides unique hyperspectral imaging simultaneously covering 25-235 µm. We synthesize images representing a deep, 1500 h deg^-2 PRIMAger survey, with realistic instrumental and confusion noise. We demonstrate that we can construct catalogues of galaxies with a high purity (>95 per cent) at a source density of 42 k deg^-2 using PRIMAger data alone. Using the XID+ deblending tool, we show that we measure fluxes with an accuracy better than 20 per cent to flux levels of 0.16, 0.80, 9.7, and 15 mJy at 47.4, 79.7, 172, and 235 µm, respectively. These are a factor of ~2 and ~3 fainter than the classical confusion limits for 72-96 and 126-235 µm, respectively. At $1.5 \le z \le 2$, we detect and accurately measure fluxes in 8-10 of the 10 channels covering 47-235 µm for sources with $2 \lesssim \log ({\rm SFR}) \lesssim 2.5$, a 0.5 dex improvement on what might be expected from the classical confusion limit. Recognizing that PRIMager will operate in a context where high-quality data will be available at other wavelengths, we investigate the benefits of introducing additional prior information. We show that by introducing even weak prior flux information when employing a higher source density catalogue (more than one source per beam), we can obtain accurate fluxes an order of magnitude below the classical confusion limit for 96-235 µm.