  We report the precise pressure dependence of FeSe from a resistivity
measurement up to 4.15 GPa. Superconducting transition temperature (T_c)
increases sensitively under pressure, but shows a plateau between 0.5-1.5 GPa.
The maximum T_c, which is determined by zero resistance, is 21 K at
approximately 3.5 GPa. The onset value reaches ~37 K at 4.15 GPa. We also
measure the nuclear spin-lattice relaxation rate 1/T_1 under pressure using
77Se--NMR measurement. 1/T_1 shows that bulk superconductivity is realized in
the zero-resistance state. The pressure dependence of 1/T_1T just above T_c
shows a plateau as well as the pressure dependence of T_c, which gives clear
evidence of the close relationship between 1/T_1T and T_c. Spin fluctuations
are suggested to contribute to the mechanism of superconductivity.
