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)))
def test_primes_firsts(self):
assert Primes.first(1) == [2]
assert Primes.first(2) == [2, 3]
assert Primes.first(5) == [2, 3, 5, 7, 11]
assert Primes.first(20)[-5:] == [53, 59, 61, 67, 71]
assert Primes.first(100)[99] == 541
assert Primes.first(20004)[79] == 409
def main():
"""
>>> main()
26033
"""
primes = Primes(10 ** 8)
remarkable_primes = []
remarkable_primes_min_sum = sys.maxsize
i = 0
while True:
if i > PRIME_INDEX_LIMIT:
last_added_prime = list_to_int(remarkable_primes.pop())
i = primes.index(last_added_prime) + 1
if len(remarkable_primes) == 0 and i == PRIME_INDEX_LIMIT:
break
new_prime = str(primes[i])
new_prime_is_remarkable = True
for prime in remarkable_primes:
if list_to_int(new_prime + prime) not in primes:
new_prime_is_remarkable = False
break
if list_to_int(prime + new_prime) not in primes:
new_prime_is_remarkable = False
break
if new_prime_is_remarkable:
remarkable_primes.append(new_prime)
if len(remarkable_primes) == LEN_PRIME_SET:
primes_sum = sum((int(p) for p in remarkable_primes))
if primes_sum < remarkable_primes_min_sum:
remarkable_primes_min_sum = primes_sum
i += 1
print(remarkable_primes_min_sum)
