We present the results of neutron detection in a laser plasma experiment with a CD$_2$ nanowire target. A hybrid semiconductor pixel detector Timepix3 covered with neutron converters was used for the detection of neutrons. D-D fusion neutrons were detected in a polyethylene converter through recoiled protons. Both the energy of recoiled protons and the time-of-flight of neutrons (and thus their energy) were determined. We report $(2.4 pm 1.8) times 10^7$ neutrons generated for 1~J of incoming laser energy. Furthermore, we proved that Timepix3 is suitable for difficult operational conditions in laser experiments.
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