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ABSTRACT 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. 

We present images obtained with LABOCA on the APEX telescope of a sample of 22 galaxies selected via their red Herschel SPIRE 250-, 350- and $$500\textrm{-}\mu\textrm{m}$$ colors. We aim to see if these luminous, rare and distant galaxies are signposting dense regions in the early Universe. Our $$870\textrm{-}\mu\textrm{m}$$ survey covers an area of $$\approx0.8\,\textrm{deg}^2$$ down to an average r.m.s. of $$3.9\,\textrm{mJy beam}^{-1}$$, with our five deepest maps going $$\approx2\times$$ deeper still. We catalog 86 DSFGs around our 'signposts', detected above a significance of $$3.5\sigma$$. This implies a $$100\pm30\%$$ over-density of $$S_{870}>8.5\,\textrm{mJy}$$ DSFGs, excluding our signposts, when comparing our number counts to those in 'blank fields'. Thus, we are $$99.93\%$$ confident that our signposts are pinpointing over-dense regions in the Universe, and $$\approx95\%$$ confident that these regions are over-dense by a factor of at least $$\ge1.5\times$$. Using template SEDs and SPIRE/LABOCA photometry we derive a median photometric redshift of $$z=3.2\pm0.2$$ for our signposts, with an interquartile range of $$z=2.8\textrm{-}3.6$$. We constrain the DSFGs likely responsible for this over-density to within $$|\Delta z|\le0.65$$ of their respective signposts. These 'associated' DSFGs are radially distributed within $$1.6\pm0.5\,\textrm{Mpc}$$ of their signposts, have median SFRs of $$\approx(1.0\pm0.2)\times10^3\,M_{\odot}\,\textrm{yr}^{-1}$$ (for a Salpeter stellar IMF) and median gas reservoirs of $$\sim1.7\times10^{11}\,M_{\odot}$$. These candidate proto-clusters have average total SFRs of at least $$\approx (2.3\pm0.5)\times10^3\,M_{\odot}\,\textrm{yr}^{-1}$$ and space densities of $$\sim9\times10^{-7}\,\textrm{Mpc}^{-3}$$, consistent with the idea that their constituents may evolve to become massive ETGs in the centers of the rich galaxy clusters we see today.