

"""simple docstring"""




def 		A    (       snake_case__      ):




			'''simple docstring'''


			SCREAMING_SNAKE_CASE__									= str(snake_case__      ).strip()
			if not bin_string:
						raise ValueError("""Empty string was passed to the function"""      )
			SCREAMING_SNAKE_CASE__									= bin_string[0] == """-"""
			if is_negative:
						SCREAMING_SNAKE_CASE__									= bin_string[1:]
			if not all(char in """01""" for char in bin_string      ):
						raise ValueError("""Non-binary value was passed to the function"""      )
			SCREAMING_SNAKE_CASE__									= 0
			for char in bin_string:
						SCREAMING_SNAKE_CASE__									= 2 * decimal_number + int(snake_case__      )
			return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
						from doctest import testmod

						testmod()





"""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))


