Why is my function using Python time limited in input value magnatude?

Question

I am trying to make a function that tests the command time in python. The function should take m,nas a parameters and calculates MODEXP(a,e,p)

Answer 1

You code runs fine on my box without hanging. As others have pointed out, it is O(2**n), hence the run time grows exponentially. Here my timing:

m = n = 2; time needed:  1.90734863281e-05
m = n = 3; time needed:  1.50203704834e-05
m = n = 4; time needed:  2.21729278564e-05
m = n = 5; time needed:  4.38690185547e-05
m = n = 6; time needed:  9.41753387451e-05
m = n = 7; time needed:  0.000232934951782
m = n = 8; time needed:  0.000643014907837
m = n = 9; time needed:  0.00198698043823
m = n = 10; time needed:  0.00656795501709
m = n = 11; time needed:  0.0229339599609
m = n = 12; time needed:  0.082200050354
m = n = 13; time needed:  0.299206972122
m = n = 14; time needed:  1.09857010841
m = n = 15; time needed:  4.06366610527
m = n = 16; time needed:  15.0994331837
m = n = 17; time needed:  56.4191129208

For m = n = 100, it would take roughly 1.3 * 10^49 seconds.