We report on the first star discovered to host a planet detected by radial velocity (RV) observations obtained within the CARMENES survey for exoplanets around M dwarfs. HD 147379 ($V = 8.9$ mag, $M = 0.58 pm 0.08$ M$_{odot}$), a bright M0.0V star at a distance of 10.7 pc, is found to undergo periodic RV variations with a semi-amplitude of $K = 5.1pm0.4$ m s$^{-1}$ and a period of $P = 86.54pm0.06$ d. The RV signal is found in our CARMENES data, which were taken between 2016 and 2017, and is supported by HIRES/Keck observations that were obtained since 2000. The RV variations are interpreted as resulting from a planet of minimum mass $m_{rm p}sin{i} = 25 pm 2$ M$_{oplus}$, 1.5 times the mass of Neptune, with an orbital semi-major axis $a = 0.32$ au and low eccentricity ($e < 0.13$). HD 147379b is orbiting inside the temperate zone around the star, where water could exist in liquid form. The RV time-series and various spectroscopic indicators show additional hints of variations at an approximate period of 21.1d (and its first harmonic), which we attribute to the rotation period of the star.
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