def main():
"""
>>> main()
134043
"""
primes = Primes(10 ** 6)
min_consecutive_valid_numbers = 4
distinct_prime_factors = 4
# next number after lower bound has to have at least distinct_prime_factors
# of odd primes as prime factors
lower_bound = (3 * 5 * 7 * 11) - 1
number = 0
consecutive_valid_numbers_count = 0
for number in count(lower_bound):
if consecutive_valid_numbers_count == min_consecutive_valid_numbers:
break
if len(set(primes.factors_of(number))) == distinct_prime_factors:
consecutive_valid_numbers_count += 1
else:
consecutive_valid_numbers_count = 0
# print first number of the consecutive numbers
print(number - distinct_prime_factors)
def main():
"""
>>> main()
6857
"""
number = 600851475143
primes = Primes(10 ** 6)
print(max(primes.factors_of(number)))
