


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

   return [i for i in range(2  ,						lowerCAmelCase_   ) if is_prime[i]]
def   _UpperCamelCase				(						lowerCAmelCase_ = 8_0_0_8_0_0  ,						lowerCAmelCase_ = 8_0_0_8_0_0   )						->int:
   UpperCAmelCase							=     degree * loga(lowerCAmelCase_   )
   UpperCAmelCase							=     int(lowerCAmelCase_   )
   UpperCAmelCase							=     calculate_prime_numbers(lowerCAmelCase_   )

   UpperCAmelCase							=     0
   UpperCAmelCase							=     0
   UpperCAmelCase							=     len(lowerCAmelCase_   ) - 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() = }""")







from math import isqrt
def   _UpperCamelCase				(						lowerCAmelCase_   )						->bool:
   return all(number % divisor != 0 for divisor in range(2  ,						isqrt(lowerCAmelCase_   ) + 1   )   )
def   _UpperCamelCase				(						lowerCAmelCase_ = 1_0**6   )						->int:
   UpperCAmelCase							=     0
   UpperCAmelCase							=     1
   UpperCAmelCase							=     7
   while prime_candidate < max_prime:
      primes_count += is_prime(lowerCAmelCase_   )

      cube_index += 1
      prime_candidate += 6 * cube_index

   return primes_count


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



