
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int				)			->						bool:

       if p < 2:
              raise ValueError('''p should not be less than 2!'''				)
       elif p == 2:
              return True

       SCREAMING_SNAKE_CASE_							:				Dict		=4
       SCREAMING_SNAKE_CASE_							:				List[Any]		=(1 << p) - 1
       for _ in range(p - 2				):
              SCREAMING_SNAKE_CASE_							:				Optional[int]		=((s * s) - 2) % m
       return s == 0


if __name__ == "__main__":
 print(lucas_lehmer_test(7))
 print(lucas_lehmer_test(11))


from math import isqrt, loga
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int				)			->						list[int]:
       SCREAMING_SNAKE_CASE_							:				int		=[True] * max_number
       for i in range(2			,							isqrt(max_number - 1				) + 1				):
              if is_prime[i]:
                     for j in range(i**2			,							UpperCAmelCase_			,							UpperCAmelCase_				):
                            SCREAMING_SNAKE_CASE_							:				Dict		=False

       return [i for i in range(2			,							UpperCAmelCase_				) if is_prime[i]]
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int = 8_0_0_8_0_0			,							UpperCAmelCase_	:     int = 8_0_0_8_0_0				)			->						int:
       SCREAMING_SNAKE_CASE_							:				str		=degree * loga(UpperCAmelCase_				)
       SCREAMING_SNAKE_CASE_							:				List[Any]		=int(UpperCAmelCase_				)
       SCREAMING_SNAKE_CASE_							:				int		=calculate_prime_numbers(UpperCAmelCase_				)

       SCREAMING_SNAKE_CASE_							:				int		=0
       SCREAMING_SNAKE_CASE_							:				List[Any]		=0
       SCREAMING_SNAKE_CASE_							:				Any		=len(UpperCAmelCase_				) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left]				)
                  + prime_numbers[left] * loga(prime_numbers[right]				)
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


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