# Searches for the first five perfect numbers.
# This version uses a multi-process pool for concurrency.

import itertools
import math   # for sqrt
import os
import time
from multiprocessing import Pool

# returns the sum of the proper divisors of n
def sum_divisors(n):
    root = int(math.sqrt(n))
    result = sum((k + n // k for k in \
             range(2, root + 1) if n % k == 0)) + 1
    if n == root * root:
        result -= root
    return result

# returns n if n is a perfect number, else None
def is_perfect_number(n):
    if n == sum_divisors(n):
        return n

# Runs the given function f, measuring how long it took to run.
# Returns the elapsed runtime at the end of the call.
def measure_runtime(f):
    start_time = time.time()
    f()
    elapsed_time = time.time() - start_time
    return elapsed_time

# Finds and prints the first 5 perfect numbers.
def find_perfect_numbers():
    print("Searching for perfect numbers on", \
          os.cpu_count(), "CPUs:")
    pool = Pool()
    results = pool.imap(is_perfect_number, itertools.count(1))
    perfects = (n for n in results if n is not None)
    first_five = itertools.islice(perfects, 5)
    for k in first_five:
        print(k)

def main():
    runtime = measure_runtime(find_perfect_numbers)
    print("time =", runtime, "sec")

main()