
from __future__ import annotations

import math


def 		UpperCAmelCase     (      a_		)						->      bool:







				"""simple docstring"""



				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


SCREAMING_SNAKE_CASE				:List[Any]									=							[num for num in range(3, 10_0001, 2) if not is_prime(num)]


def 		UpperCAmelCase     (      a_		)						->      list[int]:







				"""simple docstring"""



				if not isinstance(__UpperCamelCase						,  __UpperCamelCase		):
								raise ValueError("n must be an integer"		)
				if n <= 0:
								raise ValueError("n must be >= 0"		)

				__A       =					[]
				for num in range(len(__UpperCamelCase		)		):
								__A       =					0
								while 2 * i * i <= odd_composites[num]:
												__A       =					odd_composites[num] - 2 * i * i
												if is_prime(__UpperCamelCase		):
																break
												i += 1
								else:
												list_nums.append(odd_composites[num]		)
												if len(__UpperCamelCase		) == n:
																return list_nums

				return []


def 		UpperCAmelCase     (      )						->      int:







				"""simple docstring"""



				return compute_nums(1		)[0]


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





def A    (							__UpperCamelCase			,						__UpperCamelCase			,						__UpperCamelCase       )    ->   int:

			if exponent == 1:
						return base
			if exponent % 2 == 0:
						A__	  =     _modexpt(__UpperCamelCase			,						exponent // 2			,						__UpperCamelCase       ) % modulo_value
						return (x * x) % modulo_value
			else:
						return (base * _modexpt(__UpperCamelCase			,						exponent - 1			,						__UpperCamelCase       )) % modulo_value


def A    (							__UpperCamelCase = 1_777			,						__UpperCamelCase = 1_855			,						__UpperCamelCase = 8       )    ->   int:
			A__	  =     base
			for _ in range(1			,						__UpperCamelCase       ):
						A__	  =     _modexpt(__UpperCamelCase			,						__UpperCamelCase			,						10**digits       )

			return result


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




