Why is pow(base, exponent) is more efficient than pow(base, exponent, mod) in Python? Got you.. It’s reverse let’s see why!

Nothing fancy, just some part of pow(2, 10000) result.
[1,7,7,4,3,1,7,0,1,4,4,9,2,8,5,0,0,9,3,1,2,5,9,6,0,9,9,0,9,6,0,5,3,7,9,8,8,9,8,2,5,4,1,9,3,8,0,5,9,5,6,1,1,8,9,3,7,8,5,8,5,5,3,0,4,3,1,5,4,1,7,9,6,8,8,9,8,0,6,7,8,3,1,1,1,0,6,8,1,1,6,6,9,1,8,5,6,9,0,0,1,7,1,7,7,2,8,5,4,4,5,2,9,6,5,0,8,1,0,9,5,8,7,6,0,6,1,8,7,2,9,8,1,0,7,9,4,7,6,9,2,3,1,3,9,9,6,8,0,8,9,7,7,7,3,9,5,5,7,4,9,8,3,0,1,2,1,5,0,8,4,4,3,8,9,3,7,5,3,9,4,4,9,3,3,2,4,8,9,3,3,8,2,8,1,3,2,2,8,4,2,5,0,6,3,0,9,0,5,4,1,1,8,0,4,2,5,8,2,4,2,7,5,4,7,6,9,0,8,9,6,1,4,7,7,9,7,8,1,4,4,3,6,4,5,2,6,0,1,1,5,3,8,0,9,8,8,0,0,6,1,6,9,6,5,8,7,4,8,9,9,2,4,7,7,9,9,5,2,2,6,9,7,7,9,8,5,9,8,5,5,0,3,5,8,9,5,7,3,4,6,4,6,2,3,5,2,3,1,4,5,9,3,3,6,4,1,3,3,2,0,0,4,4,7,2,3,3,9,8,7,8,5,5,0,8,3,4,1,4,0,9,5,5,4,4,9,7,7,4,1,8,7,5,2,4,9,7,9,1,7,8,9,2,4,1,1,7,6,4,3,6,5,0,2,1,4,3,9,2,0,0,2,9,8,4,5,7,3,5,8,2,3,9,5,9,1,8,8,9,2,3,7,0,4,1,1,8,7,0,2,7,3,4,6,1,0,3,8,5,8,9,8,4,8,3,5,1,1,4,2,5,9,0,5,3,1,7,4,8,9,6,7,2,3,5,5,3,9,6,9,9,5,7,3,5,2,9,9,5,5,1,0,6,3,8,0,5,5,6,5,6,4,5,1,7,0,6,3,9,4,4,9,1,3,4,7,7,5,8,2,0,9,2,7,3,0,9,0,7,7,7,4,1,2,5,1,3,3,6,4,8,2,5,9,5,0,8,2,5,6,4,8,8,8,7,3,1,8,5,0,5,2,4,8,5,1,1,0,7,9,6,5,1,2,6,6,4,7,0,9,5,6,9,3,7,8,8,8,6,5,8,3,8,5,4,5,8,5,7,5,7,3,2,8,7,1,7,1,8,7,3,3,6,2,9,3,3,9,3,1,5,1,5,5,8,1,2,7,8,9,2,5,4,5,4,2,6,1,3,6,0,6,9,6,1,0,1,4,0,4,5,5,8,2,2,6,3,4,3,4,3,8,9,7,5,5,9,1,8,5,9,9,1,8,7,2,1,1,8,1,5,6,8,5,8,0,2,4,4,7,8,9,5,9,8,0,5,0,3,5,5,2,6,8,3,4,1,4,7,1,7,2,7,5,8,8,7,2,2,3,9,2,2,7,3,2,9,0,2,3,6,9,7,2,8,0,8,1,6,5,2,3,0,2,0,0,0,9,2,2,2,3,6,6,0,9,1,0,0,3,5,8,3,2,0,3,5,1,4,1,6,8,7,6,0,9,8,0,1,0,4,5,6,0,2,8,2,5,0,2,8,5,2,3,0,2,6,7,3,0,0,2,1,9,0,1,9,9,2,0,1,6,7,7,9,9,6,1,4,8,5,5,6,7,0,6,1,7,3,5,9,3,9,0,5,9,2,4,8,6,6,2,2,3,9,3,5,7,4,1,6,9,8,2,6,9,0,0,8,5,7,7,0,6,0,5,7,4,9,6,0,7,8,4,3,9,8,8,7,4,1,5,6,0,9,4,1,9,4,9,4,1,8,6,7,8,2,5,2,3,3,4,3,3,1,6,4,1,6,1,5,7,8,1,9,7,6,0,8,0,1,4,4,0,1,1,8,3,8,3,8,3,9,1,6,0,7,1,3,3,4,9,3,5,2,4,2,0,7,3,3,8,7,7,8,8,0,9,3,1,2,2,4,3,3,3,6,1,6,9,6,2,0,1,7,5,6,2,5,3,5,0,3,2,7,2,3,0,3,6,1,7,8,7,0,4,0,6,7,6,6,3,9,8,5,8,3,3,0,9,6,7,1,9,2,1,3,5,1,6,3,4,3,4,1,6,8,4,2,5]
//Pseudo code:base = base % n;if (exp == 0)
return 1;
else if (exp == 1)
return base;
else if (exp % 2 == 0)
return modPow(base * base % n, exp / 2, n);
else
return base * modPow(base, exp - 1, n) % n;
An example from my Interpreter.
#include<stdio.h>int modPow(int base, int exp, int n) {base = base % n;if (exp == 0)
return 1;
else if (exp == 1)
return base;
else if (exp % 2 == 0)
return modPow(base * base % n, exp / 2, n);
else
return base * modPow(base, exp - 1, n) % n;
}
int main() {

int base = 256437289;
int exp = 10;
int n = 1337;

long int result = modPow(256437289, 10, 1337);
printf("%ld", result);

return 0;
}
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