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As part of a RECONS (Research Consortium on Nearby Stars) effort to discover stars nearer than 10 pc, LHS 1565 (GJ 1061; V = 13.03; M5.5 V) has been found to be only 3.7 pc from the Sun using a combination of photometric, spectroscopic and trigonometric parallax work. It ranks as the twentieth closest stellar system and underscores the incompleteness of the nearby star sample, particularly for objects near the end of the main sequence. Ironically, this unassuming red dwarf provides a shocking reminder of how much we have yet to learn about even our nearest stellar neighbors.
Henry et al. (Tue,) studied this question.