Project Euler #10 (Python)

Question

Why is my algorithm for finding the sum of all prime numbers below 2 million so slow? I\'m a fairly beginner programmer and this is what I came up with for finding the solution:

Answer 1

Your algorithm uses trial division, which is very slow. A better algorithm uses the Sieve of Eratosthenes:

def sumPrimes(n):
    sum, sieve = 0, [True] * n
    for p in range(2, n):
        if sieve[p]:
            sum += p
            for i in range(p*p, n, p):
                sieve[i] = False
    return sum

print sumPrimes(2000000)

That should run in less than a second. If you're interested in programming with prime numbers, I modestly recommend this essay at my blog.