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NEST is a widely used tool to simulate biological spiking neural networks. Here we explain theimprovements, guided by a mathematical model of memory consumption, that enable us to exploitfor the first time the computational power of the K supercomputer for neuroscience. Multi-threadedcomponents for wiring and simulation combine 8 cores per MPI process to achieve excellent scaling.K is capable of simulating networks corresponding to a brain area with 10^8 neurons and 10^12 synapsesin the worst case scenario of random connectivity; for larger networks of the brain its hierarchicalorganization can be exploited to constrain the number of communicating computer nodes. Wediscuss the limits of the software technology, comparing maximum-□lling scaling plots for K andthe JUGENE BG/P system. The usability of these machines for network simulations has becomecomparable to running simulations on a single PC. Turn-around times in the range of minutes evenfor the largest systems enable a quasi-interactive working style and render simulations on this scalea practical tool for computational neuroscience.