Project Euler Problem 10

Project Euler problem 10 is to find the sum of all primes less than 2 million. I have written a program that does this, and it works, but it takes an excruciatingly long amount of time. What I'm asking is if there is any way I could optimize this to make it run much faster.

I wrote it in an app on my iPad called Pythonista.

def checkPrime(number):
    if number == 2:
        return True

    if number < 2:
        return False

    if number % 2 == 0:
        return False

    for i in range(3, (number**1/2)-1, 2):
        if number % i == 0:
            return False

    return True

primes = [i for i in range(10000) if checkPrime(i)]
print sum(primes)

This problem can be solved much faster with a Sieve of Eratosthenes algorithm, especially since you need every prime between 2 and n for you to sum them up.

However, there are a few optimizations you could make to your particular algorithm.

Dynamic Programming

Your code preforms some redundant calculations. For example, once you've checked if n % 2 is zero, you know n % 4, n % 6... are also zero. To avoid these calculations you could instead divide by only the prime numbers up to and including √n:

primes = [2] #define your array of prime numbers

def checkPrime(number):
    if number  number**0.5:
            break; #no need to keep going
        if number % p == 0:
            return False
    
    primes.append(number);
    return True

primes = [i for i in range(10) if checkPrime(i)]
print sum(primes)

StackExchange Code Review Q#126347, answer score: 3