
'''simple docstring'''



from __future__ import annotations

import math
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     bool:




   """simple docstring"""

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


UpperCamelCase__      :		int       							=  [num for num in range(3, 100_001, 2) if not is_prime(num)]
def    lowerCAmelCase_	(				SCREAMING_SNAKE_CASE_						)     ->     list[int]:




   """simple docstring"""

   if not isinstance(a__    ,      a__						):
      raise ValueError("""n must be an integer"""						)
   if n <= 0:
      raise ValueError("""n must be >= 0"""						)

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

   return []
def    lowerCAmelCase_	(				)     ->     int:




   """simple docstring"""
   return compute_nums(1						)[0]


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






'''simple docstring'''



import pytest
import requests

from datasets.utils.file_utils import http_head

from .utils import OfflineSimulationMode, RequestWouldHangIndefinitelyError, offline
@pytest.mark.integration
def    lowerCAmelCase_	(				)     ->     List[Any]:




   """simple docstring"""
   with offline(OfflineSimulationMode.CONNECTION_TIMES_OUT						):
      with pytest.raises(SCREAMING_SNAKE_CASE_						):
         requests.request("""GET"""    ,      """https://huggingface.co"""						)
      with pytest.raises(requests.exceptions.ConnectTimeout						):
         requests.request("""GET"""    ,      """https://huggingface.co"""    ,      timeout=1.0						)
@pytest.mark.integration
def    lowerCAmelCase_	(				)     ->     int:




   """simple docstring"""
   with offline(OfflineSimulationMode.CONNECTION_FAILS						):
      with pytest.raises(requests.exceptions.ConnectionError						):
         requests.request("""GET"""    ,      """https://huggingface.co"""						)







def    lowerCAmelCase_	(				)     ->     Optional[Any]:




   """simple docstring"""
   with offline(OfflineSimulationMode.HF_DATASETS_OFFLINE_SET_TO_1						):
      with pytest.raises(SCREAMING_SNAKE_CASE_						):
         http_head("""https://huggingface.co"""						)






