code: 
  
  
  
  
  
  
  import math
  from collections.abc import Generator
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :Generator										=     (i for i in range(1  ,						(max_n + 1) ))
      for i in (n for n in numbers if n > 1):
          for j in range(2  ,						SCREAMING_SNAKE_CASE__ ):
              if (i % j) == 0:
                  break
          else:
              yield i
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :Generator										=     (i for i in range(1  ,						(max_n + 1) ))
      for i in (n for n in numbers if n > 1):
          # only need to check for factors up to sqrt(i)
          UpperCamelCase :Union[str, Any]										=     int(math.sqrt(SCREAMING_SNAKE_CASE__ ) ) + 1
          for j in range(2  ,						SCREAMING_SNAKE_CASE__ ):
              if (i % j) == 0:
                  break
          else:
              yield i
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :Generator										=     (i for i in range(1  ,						(max_n + 1)  ,						2 ))
      # It's useless to test even numbers as they will not be prime
      if max_n > 2:
          yield 2  # Because 2 will not be tested, it's necessary to yield it now
      for i in (n for n in numbers if n > 1):
          UpperCamelCase :List[str]										=     int(math.sqrt(SCREAMING_SNAKE_CASE__ ) ) + 1
          for j in range(3  ,						SCREAMING_SNAKE_CASE__  ,						2 ):
              # As we removed the even numbers, we don't need them now
              if (i % j) == 0:
                  break
          else:
              yield i
  
  
  def 						_A     (       ):
      from timeit import timeit
  
      UpperCamelCase :Union[str, Any]										=     '''from __main__ import slow_primes, primes, fast_primes'''
      print(timeit('''slow_primes(1_000_000_000_000)'''  ,						setup=SCREAMING_SNAKE_CASE__  ,						number=1000000 ) )
      print(timeit('''primes(1_000_000_000_000)'''  ,						setup=SCREAMING_SNAKE_CASE__  ,						number=1000000 ) )
      print(timeit('''fast_primes(1_000_000_000_000)'''  ,						setup=SCREAMING_SNAKE_CASE__  ,						number=1000000 ) )
  
  
  if __name__ == "__main__":
   __snake_case							      =						int(input("""Calculate primes up to:\n>> """).strip())
   for ret in primes(number):
    print(ret)
   benchmark()
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from __future__ import annotations
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :int										=     {1}
      UpperCamelCase :Optional[int]										=     [1]
      for _ in range(2  ,						depth + 1 ):
          UpperCamelCase :Union[str, Any]										=     [*previous_coefficients, 0]
          UpperCamelCase :List[str]										=     [0, *previous_coefficients]
          UpperCamelCase :List[str]										=     []
          for x, y in zip(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ):
              coefficients.add(x + y )
              previous_coefficients.append(x + y )
      return coefficients
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			set[int] ):
      UpperCamelCase :Union[str, Any]										=     set()
      for number in unique_coefficients:
          UpperCamelCase :Optional[int]										=     2
          UpperCamelCase :List[Any]										=     number
          while divisor**2 <= copy_number:
              UpperCamelCase :List[Any]										=     0
              while copy_number % divisor == 0:
                  copy_number //= divisor
                  multiplicity += 1
              if multiplicity >= 2:
                  non_squarefrees.add(SCREAMING_SNAKE_CASE__ )
                  break
              divisor += 1
  
      return unique_coefficients.difference(SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int = 51 ):
      UpperCamelCase :Any										=     get_pascal_triangle_unique_coefficients(SCREAMING_SNAKE_CASE__ )
      UpperCamelCase :str										=     get_squarefrees(SCREAMING_SNAKE_CASE__ )
      return sum(SCREAMING_SNAKE_CASE__ )
  
  
  if __name__ == "__main__":
   print(f'''{solution() = }''')
  
  
  
  
  
  