Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number { Rm } \gg 1 and small magnetic Prandtl number { Pm } \ll 1 .
The dependence of the critical { Rm } _ { c } for dynamo on the hydrodynamic Reynolds number { Re } is obtained for 1 \lesssim { Re } \lesssim 6700 .
In the limit { Pm } \ll 1 , { Rm } _ { c } is about three times larger than for the previously well established dynamo at large and moderate Prandtl numbers : { Rm } _ { c } \lesssim 200 for { Re } \gtrsim 6000 compared to { Rm } _ { c } \sim 60 for { Pm } \geq 1 .
Is is not as yet possible to determine numerically whether the growth rate of the magnetic energy is \propto { Rm } ^ { 1 / 2 } in the limit { Rm } \to \infty , as it should if the dynamo is driven by the inertial-range motions at the resistive scale .