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Background: Carbon ion therapy has achieved satisfactory results. However, patients have a risk to get a secondary cancer. In order to estimate the risk, it is essential to understand particle transportation and nuclear reactions in the patient' s body. The particle transport Monte Carlo simulation code is a useful tool to understand them. Since the code validation for heavy ion incident reactions is not enough, the experimental data of the elementary reaction processes are needed. Materials and Methods: We measured neutron production double-differential cross-sections (DDXs) on a carbon bombarded with 430 MeV/nucleon carbon beam at PH2 beam line of HI-MAC facility in NIRS. Neutrons produced in the target were measured with NE213 liquid organic scintillators located at six angles of 15, 30, 45, 60, 75, and 90°. Results and Discussion: Neutron production double-differential cross-sections for carbon bombarded with 430 MeV/nucleon carbon ions were measured by the time-of-flight method with NE213 liquid organic scintillators at six angles of 15, 30, 45, 60, 75, and 90°. The cross sections were obtained from 1 MeV to several hundred MeV. The experimental data were compared with calculated results obtained by Monte Carlo simulation codes PHITS, Geant4, and FLUKA. Conclusion: PHITS was able to reproduce neutron production for elementary processes of carbon-carbon reaction precisely the best of three codes.