We investigated the pulsar radio luminosity ($L$), emission efficiency (ratio of radio luminosity to its spin-down power $dot{E}$), and death line in the diagram of magnetic field (B) versus spin period (P), and found that the dependence of pulsar radio luminosity on its spin-down power ($L-dot{E}$) is very weak, shown as $Lsimdot{E}^{0.06}$, which deduces an equivalent inverse correlation between emission efficiency and spin-down power as $xisim dot{E}^{-0.94}$. Furthermore, we examined the distributions of radio luminosity of millisecond and normal pulsars, and found that, for the similar spin-down powers, the radio luminosity of millisecond pulsars is about one order of magnitude lower than that of the normal pulsars. The analysis of pulsar radio flux suggests that this correlations are not due to a selective effect, but are intrinsic to the pulsar radio emission physics. Their radio radiations may be dominated by the different radiation mechanisms. The cut-off phenomenon of currently observed radio pulsars in B-P diagram is usually referred as the pulsar death line, which corresponds to $dot{E}approx 10^{30}$ erg/s and is obtained by the cut-off voltage of electron acceleration gap in the polar cap model of pulsar proposed by Ruderman and Sutherland. Observationally, this death line can be inferred by the actual observed pulsar flux $Sapprox $1mJy and 1kpc distance, together with the maximum radio emission efficiency of 1%. At present, the actual observed pulsar flux can reach 0.01mJy by FAST telescope, which will arise the observational limit of spin-down power of pulsar as low as $dot{E}approx 10^28$ erg/s. This means that the new death line is downward shifted two orders of magnitude, which might be favorably referred as the observational limit-line, and accordingly the pulsar theoretical model for the cut-off voltage of gap should be heavily modified.
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