


'''simple docstring'''
from math import sqrt


def       _lowercase							(					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(sqrt(UpperCamelCase__      ) + 1      ),					6      ):
  if number % i == 0 or number % (i + 2) == 0:
   return False
 return True


def       _lowercase							(					UpperCamelCase__							:       int = 10001      ):
 __A	:		List[str]	  =      0
 __A	:		Tuple	  =      1
 while count != nth and number < 3:
  number += 1
  if is_prime(UpperCamelCase__      ):
   count += 1
 while count != nth:
  number += 2
  if is_prime(UpperCamelCase__      ):
   count += 1
 return number


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










'''simple docstring'''
# We ignore warnings about stepping the scheduler since we step it ourselves during gradient accumulation

import warnings

from .state import AcceleratorState, GradientState


warnings.filterwarnings('ignore', category=UserWarning, module='torch.optim.lr_scheduler')

class     _lowerCamelCase       :




 '''simple docstring'''


 def __init__(   self   ,   __lowercase   ,   __lowercase   ,   __lowercase = True   ,   __lowercase = False    ):

  """simple docstring"""







  __A	:		List[str]	  =      scheduler
  __A	:		Dict	  =      optimizers if isinstance(__lowercase   ,   (list, tuple)    ) else [optimizers]
  __A	:		List[Any]	  =      split_batches
  __A	:		Any	  =      step_with_optimizer
  __A	:		List[Any]	  =      GradientState()


 def 			snake_case__ (   self   ,   *__lowercase   ,   **__lowercase    ):

  """simple docstring"""







  if not self.step_with_optimizer:
   # No link between scheduler and optimizer -> just step
   self.scheduler.step(*__lowercase   ,   **__lowercase    )
   return

  # Otherwise, first make sure the optimizer was stepped.
  if not self.gradient_state.sync_gradients:
   if self.gradient_state.adjust_scheduler:
    self.scheduler._step_count += 1
   return

  for opt in self.optimizers:
   if opt.step_was_skipped:
    return
  if self.split_batches:
   # Split batches -> the training dataloader batch size is not changed so one step per training step
   self.scheduler.step(*__lowercase   ,   **__lowercase    )
  else:
   # Otherwise the training dataloader batch size was multiplied by `num_processes`, so we need to do
   # num_processes steps per training step
   __A	:		Tuple	  =      AcceleratorState().num_processes
   for _ in range(__lowercase    ):
    # Special case when using OneCycle and `drop_last` was not used
    if hasattr(self.scheduler   ,   'total_steps'    ):
     if self.scheduler._step_count <= self.scheduler.total_steps:
      self.scheduler.step(*__lowercase   ,   **__lowercase    )
    else:
     self.scheduler.step(*__lowercase   ,   **__lowercase    )


 def 			snake_case__ (   self    ):

  """simple docstring"""







  return self.scheduler.get_last_lr()


 def 			snake_case__ (   self    ):

  """simple docstring"""







  return self.scheduler.state_dict()


 def 			snake_case__ (   self   ,   __lowercase    ):

  """simple docstring"""







  self.scheduler.load_state_dict(__lowercase    )


 def 			snake_case__ (   self    ):

  """simple docstring"""







  return self.scheduler.get_lr()







 def 			snake_case__ (   self   ,   *__lowercase   ,   **__lowercase    ):

  """simple docstring"""







  return self.scheduler.print_lr(*__lowercase   ,   **__lowercase    )






