def pollard_rho(num, c=1):
if rabin.isprime_MR(num):
return None
x = random.randint(1, num-1)
y = f(x,c,num)
d = 1
while d == 1:
d = gcd(abs(x-y), num)
if d == num:
c = c+1
return pollard_rho(num,c)
x = f(x,c,num)
y = f(f(y,c,num),c,num)
return d
def prime_factors(num):
factors = [x for x in factor(num) if rabin.isprime_MR(x)]
d = defaultdict(int)
for fact in factors:
d[fact] += 1
return d
