def prime_factors(n, primes_set):
factors = []
while n != 1:
if n in primes_set:
break
factor = brent(n)
if factor not in primes_set:
factors += prime_factors(factor, primes_set)
else:
factors.append(factor)
while n % factor == 0:
n /= factor
if n != 1:
factors.append(n)
return factors
def prime_factors(n, primes_set):
a = n
factors = []
while n != 1:
if n in primes_set:
break
factor = brent(n)
if not factor in primes_set:
factors += prime_factors(factor, primes_set)
else:
factors.append(factor)
n /= factor
if n != 1:
factors.append(n)
return set(factors)