Precise information about the composition of the Earths core is critical to understand planetary evolution and for discussing current hot topics in geodynamic behavior, such as core-mantle boundary heat flow. However, samples from deep in the Earths interior are not available, so our knowledge is based on comparison of laboratory measurements with seismological observations, informed by meteorite composition, and indications of the Earths core temperature. One of the most interesting results of such work has been the suggestion that Earths inner core must contain light elements because the density of the core, as determined from seismological measurements, is lower than the density of pure iron, its main constituent, as determined from laboratory measurements and/or theoretical work: the density deficit is now considered to be ~4%. However, this conclusion relies critically on having an accurate pressure scale to relate lab generated pressures to geological pressures. Establishing such a scale has been the subject of intensive research but still involves significant extrapolation and approximations, especially at higher pressures. Further, a pressure scale to the multi-megabar pressures is indispensable for discussing super-Earth planets. Here we establish the first primary pressure scale extending to the multi-megabar pressures of Earths core by measuring acoustic phonon velocities using inelastic scattering from a rhenium sample in a diamond anvil cell. Our new pressure scale agrees with previous primary scales at lower pressures and also shock compression experiments, but is significantly different from previous secondary and theoretical scales at Earths core pressures: previous scales have overestimated, by at least 20%, laboratory pressures at 230 gigapascals. Our new scale suggests the density deficit of the inner core is ~9%, doubling the light-element content of the core.