Are you sure that this is a time of calculating pow() and not the time of calculating decimal representation of the result?

On my computer:

>>> t = time(); a = pow(c, 2**14+1); time()-t
11.957276344299316
>>> t = time(); a = pow(c, 2**15+1); time()-t
36.08853316307068
>>> t = time(); a = pow(c, 2**16+1); time()-t
107.43462753295898

The computational complexity is O((log(c)*e)**1.5). And it needs not so much memory: around 20 MB for final result, and few times more for intermediate results, so this is not matter of swapping.