  Constraining neutrino mass remains an elusive challenge in modern physics.
Precision measurements are expected from several upcoming cosmological probes
of large-scale structure. Achieving this goal relies on an equal level of
precision from theoretical predictions of neutrino clustering. Numerical
simulations of the non-linear evolution of cold dark matter and neutrinos play
a pivotal role in this process. We incorporate neutrinos into the cosmological
N-body code CUBEP3M and discuss the challenges associated with pushing to the
extreme scales demanded by the neutrino problem. We highlight code
optimizations made to exploit modern high performance computing architectures
and present a novel method of data compression that reduces the phase-space
particle footprint from 24 bytes in single precision to roughly 9 bytes. We
scale the neutrino problem to the Tianhe-2 supercomputer and provide details of
our production run, named TianNu, which uses 86% of the machine (13,824 compute
nodes). With a total of 2.97 trillion particles, TianNu is currently the
world's largest cosmological N-body simulation and improves upon previous
neutrino simulations by two orders of magnitude in scale. We finish with a
discussion of the unanticipated computational challenges that were encountered
during the TianNu runtime.
