We report systematic measurements of ac susceptibility, nuclear-quadrupole-resonance spectrum, and nuclear-spin-lattice-relaxation time (T1) on the pressure (P)-induced heavy-fermion superconductor CeRhIn5. The temperature (T) dependence of 1/T(1) at P=1.6 GPa has revealed that antiferromagnetism (AFM) and superconductivity (SC) coexist microscopically, exhibiting the respective transition at T(N)=2.8 K and T(MF)(c)=0.9 K. It is demonstrated that SC does not yield any trace of gap opening in low-lying excitations below T(onset)(c)=2 K, but T(MF)(c)=0.9 K, followed by a T(1)T=const law. These results point to the unconventional characteristics of SC coexisting with AFM. We highlight that both of the results deserve theoretical work on the gapless nature in the low-lying excitation spectrum due to the coexistence of AFM and SC and the lack of the mean-field regime below T(onset)(c)=2 K.