为什么程序运行需要这么长时间？

Question

I'm trying to solve a question from Project Euler using Python. Why does my code take so long to run when the range of j is huge. It works just fine when j has a small range.

Answer 1

since your program has 2 for loops that fully iterate, your program time complexity is O(n**2) so it is expected to take so long time, you can do some optimizations in your code:

import math

def is_prime(number):
    for i in range(2, int(math.sqrt(number) + 1)):               
       if (number % i) == 0: 
           return False
    return True

Answer 2

Think about it logically, the larger the range, larger the number of iterations/loops for j. And then again the larger each individual number of j gets which is fed in to is_prime, the larger the i loop gets as well. Thus compounding the length of time it takes to run.

Your i loop needs to be smarter. Is there a need to check any more i numbers are factors of j once count its larger than 2? ;)