

import math







def 			A_      (    _UpperCAmelCase    ):

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







def 			A_      (    _UpperCAmelCase = 1_00_01    ):

						try:
												SCREAMING_SNAKE_CASE_: Any  		=       int(_UpperCAmelCase    )
						except (TypeError, ValueError):
												raise TypeError("Parameter nth must be int or castable to int."    ) from None
						if nth <= 0:
												raise ValueError("Parameter nth must be greater than or equal to one."    )
						SCREAMING_SNAKE_CASE_: list[int]  		=       []
						SCREAMING_SNAKE_CASE_: str  		=       2
						while len(_UpperCAmelCase    ) < nth:
												if is_prime(_UpperCAmelCase    ):
																		primes.append(_UpperCAmelCase    )
																		num += 1
												else:
																		num += 1
						return primes[len(_UpperCAmelCase    ) - 1]


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











'''simple docstring'''






from __future__ import annotations

import typing
from collections import Counter




def     snake_case_					(     lowerCAmelCase_		)->		typing.Counter[int]:





       '''simple docstring'''


       _UpperCAmelCase  :						typing.Counter[int]			     = Counter()
       for base in range(1       ,   max_perimeter + 1		):
              for perpendicular in range(lowerCAmelCase_       ,   max_perimeter + 1		):
                     _UpperCAmelCase  :						List[str]			     = (base * base + perpendicular * perpendicular) ** 0.5
                     if hypotenuse == int(lowerCAmelCase_		):
                            _UpperCAmelCase  :						Optional[Any]			     = int(base + perpendicular + hypotenuse		)
                            if perimeter > max_perimeter:
                                   continue
                            triplets[perimeter] += 1
       return triplets




def     snake_case_					(     lowerCAmelCase_ = 1000		)->		int:





       '''simple docstring'''


       _UpperCAmelCase  :						int			     = pythagorean_triple(lowerCAmelCase_		)
       return triplets.most_common(1		)[0][0]


if __name__ == "__main__":
   print(f"""Perimeter {solution()} has maximum solutions""")



