




from math import isqrt, loga



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	list[int]:
  lowerCAmelCase__				:  Dict		       =     [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      ):
        lowerCAmelCase__				:  List[str]		       =     False

  return [i for i in range(2	,      UpperCamelCase      ) if is_prime[i]]



def      __lowerCAmelCase			(					UpperCamelCase = 800800	,      UpperCamelCase = 800800      )     ->	int:
  lowerCAmelCase__				:  List[str]		       =     degree * loga(UpperCamelCase      )
  lowerCAmelCase__				:  Tuple		       =     int(UpperCamelCase      )
  lowerCAmelCase__				:  Optional[int]		       =     calculate_prime_numbers(UpperCamelCase      )

  lowerCAmelCase__				:  List[Any]		       =     0
  lowerCAmelCase__				:  Optional[int]		       =     0
  lowerCAmelCase__				:  str		       =     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() = }""")







from datetime import datetime

import matplotlib.pyplot as plt
import torch



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	str:
  for param in module.parameters():
    lowerCAmelCase__				:  int		       =     False



def      __lowerCAmelCase			(					)     ->	Optional[Any]:
  lowerCAmelCase__				:  List[Any]		       =     '''cuda''' if torch.cuda.is_available() else '''cpu'''
  if torch.backends.mps.is_available() and torch.backends.mps.is_built():
    lowerCAmelCase__				:  Optional[Any]		       =     '''mps'''
  if device == "mps":
    print(
        '''WARNING: MPS currently doesn\'t seem to work, and messes up backpropagation without any visible torch'''
        ''' errors. I recommend using CUDA on a colab notebook or CPU instead if you\'re facing inexplicable issues'''
        ''' with generations.'''      )
  return device



def      __lowerCAmelCase			(					UpperCamelCase      )     ->	List[Any]:
  lowerCAmelCase__				:  str		       =     plt.imshow(UpperCamelCase      )
  fig.axes.get_xaxis().set_visible(UpperCamelCase      )
  fig.axes.get_yaxis().set_visible(UpperCamelCase      )
  plt.show()



def      __lowerCAmelCase			(					)     ->	str:
  lowerCAmelCase__				:  Dict		       =     datetime.now()
  lowerCAmelCase__				:  Optional[int]		       =     current_time.strftime('''%H:%M:%S'''      )
  return timestamp

