  Galaxy clusters, employed by Zwicky to demonstrate the existence of dark
matter, pose new stringent tests. If merging clusters demonstrate that dark
matter is self-interacting with cross section $\sigma/m\sim 2$ cm$^2$/gr,
MACHOs, primordial black holes and light axions that build MACHOs are ruled out
as cluster dark matter. Recent strong lensing and X-ray gas data of the quite
relaxed and quite spherical cluster A1835 allow to test the cases of dark
matter with Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distribution, next
to Navarro-Frenck-White profiles. Fits to all these profiles are formally
rejected at over $5\sigma$, except in the fermionic situation. The
interpretation in terms of (nearly) Dirac neutrinos with mass of
$1.61^{+0.19}_{-0.30}$ eV/$c^2$ is consistent with results on the cluster
A1689, with the WMAP, Planck and DES dark matter fractions and with the
nondetection of neutrinoless double $\beta$-decay. The case will be tested in
the 2018 KATRIN experiment.
