1) Our current understanding of interstellar carbon isotopic fractionation hinges on the interpretation of astrochemical kinetic models. Yet, the various reactions included carry large uncertainties in their (estimated) rate coefficients, notably those involving C with C2

2) In this work, we report accurate theoretical thermal rate coefficients as a function of the temperature for all possible gas-phase isotope-exchange reactions of C with C2

3) By relying on the large masses of the atoms involved, we employ a variation of the quasiclassical trajectory method, with the previously obtained (mass-independent) potential energy surfaces of C3 dictating the forces between the colliding partners

4) Apart from the proper kinetic attributes, we also provide equilibrium constants for these processes, unraveling their increased efficiency into 13C incorporation at low temperatures.

5) The present theoretical results strongly support the previous suggestions made that these C+C2 reactions may indeed act as important routes in the overall interstellar carbon fractionation chemistry, notably in low-temperature carbon-rich environments.

6) The calculated rate constants and the three-parameter Arrhenius-Kooij formulas so derived can readily be introduced in astrochemical models of cold dense clouds