"""Solves Problem 10 for Project Euler."""
    import math

    def is_prime(candidate, known_primes):
        """Determines whether candidate is prime by trial division using \
        known_primes.

        For this function to work, known_primes *must* be accurate.
        """
        last_possible = math.sqrt(candidate)
        for current_prime in known_primes:
            if current_prime > last_possible:
                break
            if not candidate % current_prime:
                return False
        return True

    def primes_generator(upper_bound):
        """A generator for all the primes < upper_bound."""
        candidates = xrange(2, upper_bound)
        primes = []
        for n in candidates:
            if is_prime(n, primes):
                primes.append(n)
                yield n

    def problem_10():
        """Sum the primes less than 2 million."""
        return sum(primes_generator(2000000))

    if __name__ == '__main__':
        print problem_10()