Finding high-redshift (z ≫ 4) dusty star-forming galaxies is extremely challenging. It has recently been suggested that millimeter selections may be the best approach since the negative K-correction makes galaxies at a given far-infrared luminosity brighter at z ≳ 4 than those at z = 2-3. Here we analyze this issue using a deep Atacama Large Millimeter/submillimeter Array (ALMA) 2 mm sample obtained by targeting ALMA 870 μm priors (these priors were the result of targeting SCUBA-2 850 μm sources) in the GOODS-S. We construct prior-based 2 mm galaxy number counts and compare them with published blank field-based 2 mm counts, finding good agreement down to 0.2 mJy. Only a fraction of the current 2 mm extragalactic background light is resolved, and we estimate what observational depths may be needed to resolve it fully. By complementing the 2 mm ALMA data with a deep SCUBA-2 450 μm sample, we exploit the steep gradient with a redshift of the 2 mm-450 μm flux density ratio to estimate redshifts for those galaxies without spectroscopic or robust optical/near-infrared photometric redshifts. Our observations measure galaxies with star formation rates in excess of 250 M ⊙ yr−1. For these galaxies, the star formation rate densities fall by a factor of 9 from z = 2-3 to z = 5-6.