如何加快寻找过程？

Question

I was doing Problem 7 on Project Euler when I ran into a problem. My code was taking to long to finish. Here is my code.

def Problem7():
    num = 0
    p = 0 
    while p < 10002 :
        prime = True
        for i in range(2,num):
            if (num%i==0):
                prime = False
        if prime:
           print(num)
           p = p + 1
        num = num + 1
Problem7()

How do I make it faster? Is there another way?

Answer 1

You should make your life easier and print the prime count at the end which is what I suspect the p variable is storing.

As noted in comments, you can eliminate a lot of calculations with a smarter algorithm.

1: Check if the number is even (num%2) (if so, not prime)

2: While divisor is less than or equal to square root and prime ==True, test divisor

3: If still not prime, increment by 2 so you only test odd numbers (All evens were checked with num%2)

If you wanted to get super efficient, every number that is not prime has at least one prime factor, so you could store each prime that you find in an array and only check those up to the highest in the array... But that is a lot of extra coding that is not necessary to this problem. Using the above logic I've found the first 10,000 primes in a matter of a few seconds on a test run.

If you think of the number 100, your logic tests 99 possible divisors. The above logic tests only 2 then stops. Worst case of going to the square root would be only 2,3,5,7,9... 5 calculations instead of 99.

Answer 2

I used the following method to check if number is prime (runs in 0m0.612s):

import math

def is_prime(num):
    if num == 0 or num == 1:
        return False
    if num == 2:
        return True
    temp = 2
    while temp < math.sqrt(num) + 1:
        if num % temp == 0:
            return False
        temp += 1

    return True