

"""simple docstring"""




from __future__ import annotations

def 		A    (       snake_case__						,			snake_case__						,			snake_case__						,			):




			'''simple docstring'''


			if not all((nth_term, start_term_a, common_ratio_r)      ):
						return []
			SCREAMING_SNAKE_CASE__									= []
			SCREAMING_SNAKE_CASE__									= 1
			SCREAMING_SNAKE_CASE__									= common_ratio_r
			for _ in range(int(_UpperCamelCase      )      ):
						if not series:
									series.append(_UpperCamelCase      )
						else:
									power += 1
									series.append(float(start_term_a * multiple      )      )
									SCREAMING_SNAKE_CASE__									= pow(float(_UpperCamelCase      )						,			_UpperCamelCase      )
			return series


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						A_							:     Union[str, Any]     =	float(input("Enter the last number (n term) of the Geometric Series"))
						A_							:     List[Any]     =	float(input("Enter the starting term (a) of the Geometric Series"))
						A_							:     str     =	float(
						    input("Enter the common ratio between two terms (r) of the Geometric Series")
						)
						print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
						print(geometric_series(nth_term, start_term_a, common_ratio_r))





"""simple docstring"""




import math

def 		A    (       snake_case__      ):




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

def 		A    (       snake_case__ = 10_00						,			snake_case__ = 10_00      ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__									= [0, 0, 0]  # length, a, b
			for a in range((a_limit * -1) + 1						,			snake_case__      ):
						for b in range(2						,			snake_case__      ):
									if is_prime(snake_case__      ):
												SCREAMING_SNAKE_CASE__									= 0
												SCREAMING_SNAKE_CASE__									= 0
												while is_prime((n**2) + (a * n) + b      ):
															count += 1
															n += 1
												if count > longest[0]:
															SCREAMING_SNAKE_CASE__									= [count, a, b]
			SCREAMING_SNAKE_CASE__									= longest[1] * longest[2]
			return ans


if __name__ == "__main__":
						print(solution(1_000, 1_000))


