A close win for finding the sum of the sum of all prime factors from 2-N the fastest

no_cigar.py

# @timeit
# the original one
def get_prime_factor_sum(row):
    total = 0
    primes = {}
    for prime_number in range(2, row + 1):
        if prime_number in primes:
            continue
        next_exponent = prime_number
        for prime_multiple in range(prime_number, row + 1, prime_number):
            if prime_multiple not in primes:
                primes[prime_multiple] = False
                if prime_multiple == next_exponent:
                    total += prime_number * (row // prime_multiple)
                    next_exponent *= prime_number
    return total


# the newer better version
def get_prime_factor_sum_2(row):
    total = handle_evens(row)
    primes = {}
    for prime_number in range(3, row + 1, 2):
        if prime_number in primes:
            continue
        next_exponent = prime_number
        step = prime_number * 2
        for prime_multiple in range(prime_number, row + 1, step):
            if prime_multiple not in primes:
                primes[prime_multiple] = False

                if prime_multiple == next_exponent:
                    total += prime_number * (row // prime_multiple)
                    next_exponent *= prime_number

    return total


def handle_evens(row):
    next_exponent = 2
    total = 0
    while next_exponent <= row:
        total += 2 * (row // next_exponent)
        next_exponent *= 2
    return total

print(get_prime_factor_sum_2(1000000))

#broken_bitset_attempt
def get_prime_factor_sum_3(row):
    total = handle_evens(row)
    primes = 0
    for prime_number in range(3, row + 1, 2):
        if (prime_number & ( 1 << primes)) > 0:
            continue
        next_exponent = prime_number
        step = prime_number * 2
        for prime_multiple in range(prime_number, row + 1, step):
            if (prime_multiple & ( 1 << primes)) > 0:
                primes |= (1 << prime_multiple)
 
                if prime_multiple == next_exponent:
                    total += prime_number * (row // prime_multiple)
                    next_exponent *= prime_number
 
    return total