






'''simple docstring'''







import random

from .binary_exp_mod import bin_exp_mod





def 			SCREAMING_SNAKE_CASE_	(UpperCamelCase    ,      UpperCamelCase=1000				)				->	Any:
							if n < 2:
														return False

							if n % 2 == 0:
														return n == 2

							# this means n is odd
							lowerCamelCase__ :     List[str]	  =	n - 1
							lowerCamelCase__ :     Union[str, Any]	  =	0
							while d % 2 == 0:
														d /= 2
														exp += 1

							# n - 1=d*(2**exp)
							lowerCamelCase__ :     Optional[Any]	  =	0
							while count < prec:
														lowerCamelCase__ :     Dict	  =	random.randint(2    ,      n - 1				)
														lowerCamelCase__ :     Tuple	  =	bin_exp_mod(UpperCamelCase    ,      UpperCamelCase    ,      UpperCamelCase				)
														if b != 1:
																					lowerCamelCase__ :     int	  =	True
																					for _ in range(UpperCamelCase				):
																												if b == n - 1:
																																			lowerCamelCase__ :     Dict	  =	False
																																			break
																												lowerCamelCase__ :     Tuple	  =	b * b
																												b %= n
																					if flag:
																												return False
																					count += 1
							return True


if __name__ == "__main__":
			_A     :      Any   					=abs(int(input('''Enter bound : ''').strip()))
			print('''Here\'s the list of primes:''')
			print(''', '''.join(str(i) for i in range(n + 1) if is_prime_big(i)))









'''simple docstring'''







from __future__ import annotations





def 			SCREAMING_SNAKE_CASE_	(UpperCamelCase    ,      UpperCamelCase				)				->	list[str]:
							if nth_term == "":
														return [""]
							lowerCamelCase__ :     str	  =	int(UpperCamelCase				)
							lowerCamelCase__ :     Union[str, Any]	  =	int(UpperCamelCase				)
							lowerCamelCase__ :     list[str]	  =	[]
							for temp in range(int(UpperCamelCase				)				):
														series.append(f'''1 / {pow(temp + 1    ,      int(UpperCamelCase				)				)}''' if series else """1"""				)
							return series


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			_A     :      Optional[Any]   					=int(input('''Enter the last number (nth term) of the P-Series'''))
			_A     :      List[str]   					=int(input('''Enter the power for  P-Series'''))
			print('''Formula of P-Series => 1+1/2^p+1/3^p ..... 1/n^p''')
			print(p_series(nth_term, power))

