def factors_of_a_number(n):
prime_candidates = primes_util.erastot_sieve(int(round(n**0.5)))
current = int(n)
factors = {}
while(current > 1):
if primes_util.is_prime(current):
prime = current
if not current in factors:
factors[current] = 1
else:
factors[current] = factors[current]+1
break
for prime in prime_candidates:
if current % prime == 0: #if the remainder of the division is 0, it's a divisor
if not prime in factors:
factors[prime] = 1
else:
factors[prime] = factors[prime]+1
current = current/prime
break
return factors
''' The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. ''' import primes_util print reduce(lambda x,y: x+y, primes_util.erastot_sieve(2000000))
