Question

Here are two programs that naively calculate the number of prime numbers <= n.
One is in Python and the other is in Java.

public class prime{
    public static void main(String args[]){
        int n = Integer.parseInt(args[0]);
        int nps = 0;
 boolean isp;

        for(int i = 1; i <= n; i++){
            isp = true;

            for(int k = 2; k < i; k++){
               if( (i*1.0 / k) == (i/k) ) isp = false;
            }
            if(isp){nps++;}
 }
        System.out.println(nps);
    }
}


`#!/usr/bin/python`                                                                                                                                        
import sys
n = int(sys.argv[1])
nps = 0

for i in range(1,n+1):
    isp = True
    for k in range(2,i):
        if( (i*1.0 / k) == (i/k) ): isp = False
    if isp == True: nps = nps + 1
print nps

Running them on n=10000 I get the following timings.
shell:~$ time python prime.py 10000 && time java prime 10000
1230

real 0m49.833s
user 0m49.815s
sys 0m0.012s
1230

real 0m1.491s
user 0m1.468s
sys 0m0.016s

Am I using for loops in python in an incorrect manner here or is python actually just this much slower?

I’m not looking for an answer that is specifically crafted for calculating primes but rather I am wondering if python code is typically utilized in a smarter fashion.

The Java code was compiled with
javac 1.6.0_20
Run with java version “1.6.0_18”
OpenJDK Runtime Environment (IcedTea6 1.8.1) (6b18-1.8.1-0ubuntu1~9.10.1)
OpenJDK Client VM (build 16.0-b13, mixed mode, sharing)

Python is:
Python 2.6.4 (r264:75706, Dec 7 2009, 18:45:15)

Answer 1

As has been pointed out, straight Python really isn’t made for this sort of thing. That the prime checking algorithm is naive is also not the point. However, with two simple things I was able to greatly reduce the time in Python while using the original algorithm.

First, put everything inside of a function, call it main() or something. This decreased the time on my machine in Python from 20.6 seconds to 14.54 seconds. Doing things globally is slower than doing them in a function.

Second, use Psyco, a JIT compiler. This requires adding two lines to the top of the file (and of course having psyco installed):

import psyco
psyco.full()

This brought the final time to 2.77 seconds.

One last note. I decided for kicks to use Cython on this and got the time down to 0.8533. However, knowing how to make the few changes to make it fast Cython code isn’t something that I recommend for the casual user.