Aims: We predict the exoplanet yield of a space-based mid-infrared nulling interferometer using Monte Carlo simulations. We quantify the number and properties of detectable exoplanets and identify those target stars that have the highest or most complete detection rate. We investigate how changes in the underlying technical assumptions and uncertainties in the underlying planet population impact the scientific return. Methods: We simulated $2000$ exoplanetary systems, based on planet occurrence statistics from Kepler with randomly orientated orbits and uniformly distributed albedos around each of $326$ nearby ($d < 20~text{pc}$) stars. Assuming thermal equilibrium and blackbody emission, together with the limiting spatial resolution and sensitivity of our simulated instrument in the three specific bands $5.6$, $10.0$, and $15.0~mutext{m}$, we quantified the number of detectable exoplanets as a function of their radii and equilibrium temperatures. Results: Approximately $sim315_{-77}^{+113}$ exoplanets, with radii $0.5~R_text{Earth} leq R_text{p} leq 6~R_text{Earth}$, were detected in at least one band and half were detected in all three bands during $sim0.52$ years of mission time assuming throughputs $3.5$ times worse than those for the James Webb Space Telescope and $sim40%$ overheads. Accounting for stellar leakage and (unknown) exozodiacal light, the discovery phase of the mission very likely requires $2$ - $3$ years in total. Roughly $85$ planets could be habitable ($0.5~R_text{Earth} leq R_text{p} leq 1.75~R_text{Earth}$ and $200~text{K} leq T_text{eq} leq 450~text{K}$) and are prime targets for spectroscopic observations in a second mission phase.
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