Aleksandar Donev,1,2 Frank H. Stillinger,3 and Salvatore Torquato1,2,3 1Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA 2PRISM, Princeton University, Princeton, New Jersey 08544, USA 3Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA Received 15 April 2005; published 26 August 2005. Phys. Rev. Lett. 95, 090604 (2005). Abstract We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically augmented surface area rather than the volume of the window. The structure factor shows an unusual nonanalytic linear dependence near the origin, S(k)~|k|. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, h(r)~-r-4, and a long-ranged direct correlation function c(r).