


'''simple docstring'''

from __future__ import annotations

import math





def __snake_case      (   UpperCAmelCase_		:		int	):

 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(UpperCAmelCase_	) + 1	)      ,       6	):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True


a_						:       str      			=				[num for num in range(3, 100001, 2) if not is_prime(num)]





def __snake_case      (   UpperCAmelCase_		:		int	):
 if not isinstance(UpperCAmelCase_      ,       UpperCAmelCase_	):
  raise ValueError("n must be an integer"	)
 if n <= 0:
  raise ValueError("n must be >= 0"	)

 lowerCamelCase_  				=						[]
 for num in range(len(UpperCAmelCase_	)	):
  lowerCamelCase_  				=						0
  while 2 * i * i <= odd_composites[num]:
   lowerCamelCase_  				=						odd_composites[num] - 2 * i * i
   if is_prime(UpperCAmelCase_	):
    break
   i += 1
  else:
   list_nums.append(odd_composites[num]	)
   if len(UpperCAmelCase_	) == n:
    return list_nums

 return []





def __snake_case      (   ):
 return compute_nums(1	)[0]


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







'''simple docstring'''

import math





def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		float	):
 return math.pow(UpperCAmelCase_      ,       2	) - a





def __snake_case      (   UpperCAmelCase_		:		float	):
 return 2 * x





def __snake_case      (   UpperCAmelCase_		:		float	):
 lowerCamelCase_  				=						2.0

 while start <= a:
  lowerCamelCase_  				=						math.pow(UpperCAmelCase_      ,       2	)

 return start





def __snake_case      (   UpperCAmelCase_		:		float      ,       UpperCAmelCase_		:		int = 9999      ,       UpperCAmelCase_		:		float = 0.00_0000_0000_0001	):

 if a < 0:
  raise ValueError("math domain error"	)

 lowerCamelCase_  				=						get_initial_point(UpperCAmelCase_	)

 for _ in range(UpperCAmelCase_	):
  lowerCamelCase_  				=						value
  lowerCamelCase_  				=						value - fx(UpperCAmelCase_      ,       UpperCAmelCase_	) / fx_derivative(UpperCAmelCase_	)
  if abs(prev_value - value	) < tolerance:
   return value

 return value


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

     testmod()



