






"""simple docstring"""





import math
import unittest







def      lowerCamelCase__       (							_lowerCamelCase       :		int )      ->				bool:
  assert isinstance(_lowerCamelCase		,				_lowerCamelCase ) and (
      number >= 0
  ), "'number' must been an int and positive"

  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5		,				int(math.sqrt(_lowerCamelCase ) + 1 )		,				6 ):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True






class      a						(					unittest.TestCase		):






    def    UpperCamelCase       (       self     :							Optional[Any]					)     ->		int:
      self.assertTrue(is_prime(2					)					)
      self.assertTrue(is_prime(3					)					)
      self.assertTrue(is_prime(5					)					)
      self.assertTrue(is_prime(7					)					)
      self.assertTrue(is_prime(11					)					)
      self.assertTrue(is_prime(13					)					)
      self.assertTrue(is_prime(17					)					)
      self.assertTrue(is_prime(19					)					)
      self.assertTrue(is_prime(23					)					)
      self.assertTrue(is_prime(29					)					)






    def    UpperCamelCase       (       self     :							List[str]					)     ->		str:
      with self.assertRaises(__SCREAMING_SNAKE_CASE					):
        is_prime(-19					)
      self.assertFalse(
          is_prime(0					)       ,						'Zero doesn\'t have any positive factors, primes must have exactly two.'       ,						)
      self.assertFalse(
          is_prime(1					)       ,						'One only has 1 positive factor, primes must have exactly two.'       ,						)
      self.assertFalse(is_prime(2 * 2					)					)
      self.assertFalse(is_prime(2 * 3					)					)
      self.assertFalse(is_prime(3 * 3					)					)
      self.assertFalse(is_prime(3 * 5					)					)
      self.assertFalse(is_prime(3 * 5 * 7					)					)


if __name__ == "__main__":
  unittest.main()












"""simple docstring"""





from __future__ import annotations







def      lowerCamelCase__       (							_lowerCamelCase       :		int )      ->				list[int]:
  lowerCamelCase_         =						[True] * limit
  lowerCamelCase_         =						False
  lowerCamelCase_         =						False
  lowerCamelCase_         =						True

  for i in range(3		,				int(limit**0.5 + 1 )		,				2 ):
    lowerCamelCase_         =						i * 2
    while index < limit:
      lowerCamelCase_         =						False
      lowerCamelCase_         =						index + i

  lowerCamelCase_         =						[2]

  for i in range(3		,				_lowerCamelCase		,				2 ):
    if is_prime[i]:
      primes.append(_lowerCamelCase )

  return primes







def      lowerCamelCase__       (							_lowerCamelCase       :		int = 1000000 )      ->				int:
  lowerCamelCase_         =						prime_sieve(_lowerCamelCase )
  lowerCamelCase_         =						0
  lowerCamelCase_         =						0

  for i in range(len(_lowerCamelCase ) ):
    for j in range(i + length		,				len(_lowerCamelCase ) ):
      lowerCamelCase_         =						sum(primes[i:j] )
      if sol >= ceiling:
        break

      if sol in primes:
        lowerCamelCase_         =						j - i
        lowerCamelCase_         =						sol

  return largest


if __name__ == "__main__":
  print(F'''{solution() = }''')




