


'''simple docstring'''







from __future__ import annotations






def 				lowerCAmelCase__	(    lowerCamelCase					:      int       ):
							_A					:     Optional[int]     = [True] * limit
							_A					:     Any     = False
							_A					:     Optional[int]     = False
							_A					:     Tuple     = True

							for i in range(3  ,int(limit**0.5 + 1       )  ,2       ):
														_A					:     Dict     = i * 2
														while index < limit:
																					_A					:     List[Any]     = False
																					_A					:     Optional[int]     = index + i

							_A					:     Optional[int]     = [2]

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

							return primes






def 				lowerCAmelCase__	(    lowerCamelCase					:      int = 1000000       ):
							_A					:     List[str]     = prime_sieve(lowerCamelCase       )
							_A					:     Any     = 0
							_A					:     str     = 0

							for i in range(len(lowerCamelCase       )       ):
														for j in range(i + length  ,len(lowerCamelCase       )       ):
																					_A					:     List[str]     = sum(primes[i:j]       )
																					if sol >= ceiling:
																												break

																					if sol in primes:
																												_A					:     Tuple     = j - i
																												_A					:     Any     = sol

							return largest


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










'''simple docstring'''







def 				lowerCAmelCase__	(    lowerCamelCase					:      int = 10       ):
       if not isinstance(lowerCamelCase  ,lowerCamelCase       ) or n < 0:
              raise ValueError('Invalid input'       )
       _A					:     Optional[Any]     = 10**n
       _A					:     List[str]     = 28433 * (pow(2  ,7830457  ,lowerCamelCase       )) + 1
       return str(number % modulus       )


if __name__ == "__main__":
   from doctest import testmod

   testmod()
   print(f"""{solution(10) = }""")






