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We measured the electrical resistivity of iron and iron-silicon alloy to 100 GPa. The resistivity of iron was also calculated to core pressures. Combined with the first geophysical model accounting for saturation resistivity of core metal, the present results show that the thermal conductivity of the outermost core is greater than 90 W/m/K. These values are significantly higher than conventional estimates, implying rapid secular core cooling, an inner core younger than 1 Ga, and ubiquitous melting of the lowermost mantle during the early Earth. An enhanced conductivity with depth suppresses convection in the deep core, such that its center may have been stably stratified prior to the onset of inner core crystallization. A present heat flow in excess of 10 TW is likely required to explain the observed dynamo characteristics.