The maximization of repeater spacing has been investigated where multi-pumping Raman amplifier has been employed with equal pumping powers and equal spacing of pumping wavelength. The problem is processed; employing two coupled nonlinear different equations of first order taking into account both pump-pump interactions and signal-signal interactions along the fiber. These two equations are processed rigorously using accurate software based on Runge-Kutta technique of fourth order. Wide gain of the amplifier is considered where two sets of pumps N_R {5,10} are investigated. The gain coefficient is cast under polynomial forms. The pumping wavelength l_R is over the range 1.40 £ l_R, mm £ 1.44 and the channel wavelength l_s is over the range 1.45 £ l_s, mm £ 1.65. Two multiplexing techniques are processed in long-haul transmission cables where number of channels is up to 10000 in ultra-wide wavelength division multiplexing (UW-WDM) with number of links up to 480. The problem is investigated over wide ranges of affecting sets of parameters. The present investigation has clarified vital causes that affect both Raman gain and the repeater spacing up to 360 km. The investigation of the flatness of the gain constant has indicated that the Raman pumps should be distributed over wide range of pumping wavelength before the starting of the channels wavelength range.