  The dynamo driven by the magnetorotational instability (MRI) is believed to
play an important role in the dynamics of accretion discs and may also explain
the origin of the extreme magnetic fields present in magnetars. Its saturation
level is an important open question known to be particularly sensitive to the
diffusive processes through the magnetic Prandtl number Pm (the ratio of
viscosity to resistivity). Despite its relevance to proto-neutron stars and
neutron star merger remnants, the numerically challenging regime of high Pm is
still largely unknown. Using zero-net flux shearing box simulations in the
incompressible approximation, we studied MRI-driven dynamos at unprecedentedly
high values of Pm reaching 256. The simulations show that the stress and
turbulent energies are proportional to Pm up to moderately high values
($\mathrm{Pm} \sim 50$). At higher Pm, they transition to a new regime
consistent with a plateau independent of Pm for $\rm Pm \gtrsim 100$. This
trend is independent of the Reynolds number, which may suggest an asymptotic
regime where the energy injection and dissipation are independent of the
diffusive processes. Interestingly, large values of Pm not only lead to intense
small-scale magnetic fields but also to a more efficient dynamo at the largest
scales of the box.
