The group Out(F_2) of outer-automorphisms of F_2 the rank 2 free group acts naturally on the PSL(2,C)-character variety of F_2. To study the dynamical property of Out(F_2)-action, Bowditch's Q-condition and the primitive stable condition on a representation from F_2 to PSL(2,C) have been introduced by Bowditch (generalized by Tan-Wong-Zhang) and by Minsky, respectively. Each one of them can characterize an open subset of the character variety on which Out(F_2) acts properly discontinuously. These two open sets are both candidates for the maximal domain of discontinuity for the Out(F_2)-action. In a joint work with Jaejeong Lee, we show that these two conditions are equivalent to each other.