We report a series of numerical simulations showing that the critical magnetic Reynolds number \text { Rm } _ { \text { c } } for the nonhelical small-scale dynamo depends on the Reynolds number Re .
Namely , the dynamo is shut down if the magnetic Prandtl number \text { Pr } _ { \text { m } } = \text { Rm } / \text { Re } 
is less than some critical value \text { Pr } _ { \text { m,c } } \lesssim 1 
even for Rm for which dynamo exists at \text { Pr } _ { \text { m } } \geq 1 .
We argue that , in the limit of \text { Re } \to \infty , a finite \text { Pr } _ { \text { m,c } } may exist .
The second possibility is that \text { Pr } _ { \text { m,c } } \to 0 as \text { Re } \to \infty , while \text { Rm } _ { \text { c } } tends to a very large constant value inaccessible at current resolutions .
If there is a finite \text { Pr } _ { \text { m,c } } , the dynamo is sustainable only if magnetic fields can exist at scales smaller than the flow scale , i.e. , it is always effectively a large- \text { Pr } _ { \text { m } } dynamo .
If there is a finite \text { Rm } _ { \text { c } } , our results provide a lower bound : \text { Rm } _ { \text { c } } \gtrsim 220 for \text { Pr } _ { \text { m } } \leq 1 / 8 .
This is larger than Rm in many planets and in all liquid-metal experiments .