


'''simple docstring'''






import random


def A_       (					__SCREAMING_SNAKE_CASE			:       int							)  ->	bool:
					__SCREAMING_SNAKE_CASE       :				Optional[Any]       =			num - 1
					__SCREAMING_SNAKE_CASE       :				Optional[Any]       =			0

					while s % 2 == 0:
										__SCREAMING_SNAKE_CASE       :				Dict       =			s // 2
										t += 1

					for _ in range(5							):
										__SCREAMING_SNAKE_CASE       :				Any       =			random.randrange(2						, num - 1							)
										__SCREAMING_SNAKE_CASE       :				str       =			pow(__SCREAMING_SNAKE_CASE						, __SCREAMING_SNAKE_CASE						, __SCREAMING_SNAKE_CASE							)
										if v != 1:
															__SCREAMING_SNAKE_CASE       :				str       =			0
															while v != (num - 1):
																				if i == t - 1:
																									return False
																				else:
																									__SCREAMING_SNAKE_CASE       :				Any       =			i + 1
																									__SCREAMING_SNAKE_CASE       :				List[str]       =			(v**2) % num
					return True


def A_       (					__SCREAMING_SNAKE_CASE			:       str							)  ->	bool:



					if num < 2:
										return False

					__SCREAMING_SNAKE_CASE       :				Tuple       =			[
					    2,
					    3,
					    5,
					    7,
					    11,
					    13,
					    17,
					    19,
					    23,
					    29,
					    31,
					    37,
					    41,
					    43,
					    47,
					    53,
					    59,
					    61,
					    67,
					    71,
					    73,
					    79,
					    83,
					    89,
					    97,
					    1_01,
					    1_03,
					    1_07,
					    1_09,
					    1_13,
					    1_27,
					    1_31,
					    1_37,
					    1_39,
					    1_49,
					    1_51,
					    1_57,
					    1_63,
					    1_67,
					    1_73,
					    1_79,
					    1_81,
					    1_91,
					    1_93,
					    1_97,
					    1_99,
					    2_11,
					    2_23,
					    2_27,
					    2_29,
					    2_33,
					    2_39,
					    2_41,
					    2_51,
					    2_57,
					    2_63,
					    2_69,
					    2_71,
					    2_77,
					    2_81,
					    2_83,
					    2_93,
					    3_07,
					    3_11,
					    3_13,
					    3_17,
					    3_31,
					    3_37,
					    3_47,
					    3_49,
					    3_53,
					    3_59,
					    3_67,
					    3_73,
					    3_79,
					    3_83,
					    3_89,
					    3_97,
					    4_01,
					    4_09,
					    4_19,
					    4_21,
					    4_31,
					    4_33,
					    4_39,
					    4_43,
					    4_49,
					    4_57,
					    4_61,
					    4_63,
					    4_67,
					    4_79,
					    4_87,
					    4_91,
					    4_99,
					    5_03,
					    5_09,
					    5_21,
					    5_23,
					    5_41,
					    5_47,
					    5_57,
					    5_63,
					    5_69,
					    5_71,
					    5_77,
					    5_87,
					    5_93,
					    5_99,
					    6_01,
					    6_07,
					    6_13,
					    6_17,
					    6_19,
					    6_31,
					    6_41,
					    6_43,
					    6_47,
					    6_53,
					    6_59,
					    6_61,
					    6_73,
					    6_77,
					    6_83,
					    6_91,
					    7_01,
					    7_09,
					    7_19,
					    7_27,
					    7_33,
					    7_39,
					    7_43,
					    7_51,
					    7_57,
					    7_61,
					    7_69,
					    7_73,
					    7_87,
					    7_97,
					    8_09,
					    8_11,
					    8_21,
					    8_23,
					    8_27,
					    8_29,
					    8_39,
					    8_53,
					    8_57,
					    8_59,
					    8_63,
					    8_77,
					    8_81,
					    8_83,
					    8_87,
					    9_07,
					    9_11,
					    9_19,
					    9_29,
					    9_37,
					    9_41,
					    9_47,
					    9_53,
					    9_67,
					    9_71,
					    9_77,
					    9_83,
					    9_91,
					    9_97,
					]

					if num in low_primes:
										return True

					for prime in low_primes:
										if (num % prime) == 0:
															return False

					return rabin_miller(__SCREAMING_SNAKE_CASE							)


def A_       (					__SCREAMING_SNAKE_CASE			:       Optional[int] = 10_24							)  ->	int:



					while True:
										__SCREAMING_SNAKE_CASE       :				Any       =			random.randrange(2 ** (keysize - 1)						, 2 ** (keysize)							)
										if is_prime_low_num(__SCREAMING_SNAKE_CASE							):
															return num


if __name__ == "__main__":
						_A			  =  generate_large_prime()
						print(("""Prime number:""", num))
						print(("""is_prime_low_num:""", is_prime_low_num(num)))









def  __magic_name__  (				lowercase				)				-> list:

							"""simple docstring"""



							if n_term == "":
														return []
							lowercase_	:   list  				=     []
							for temp in range(int(lowercase				)				):
														series.append(f"""1/{temp + 1}""" if series else """1"""				)
							return series


if __name__ == "__main__":
							UpperCAmelCase_							=				input("""Enter the last number (nth term) of the Harmonic Series""")
							print("""Formula of Harmonic Series => 1+1/2+1/3 ..... 1/n""")
							print(harmonic_series(nth_term))