




'''simple docstring'''






import math

def      __lowerCAmelCase   (       snake_case__		):

			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      __lowerCAmelCase   (       snake_case__ = 1_000   , snake_case__ = 1_000		):
			__UpperCamelCase :     Dict										=  [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__		):
												__UpperCamelCase :     Dict										=  0
												__UpperCamelCase :     Optional[int]										=  0
												while is_prime((n**2) + (a * n) + b		):
															count += 1
															n += 1
												if count > longest[0]:
															__UpperCamelCase :     Union[str, Any]										=  [count, a, b]
			__UpperCamelCase :     Dict										=  longest[1] * longest[2]
			return ans


if __name__ == "__main__":
				print(solution(1000, 1000))









'''simple docstring'''






import itertools

def      __lowerCAmelCase   (       snake_case__		):
			return (
			    int("".join(combination[0:2]		)		) * int("".join(combination[2:5]		)		)
			    == int("".join(combination[5:9]		)		)
			) or (
			    int("".join(combination[0]		)		) * int("".join(combination[1:5]		)		)
			    == int("".join(combination[5:9]		)		)
			)

def      __lowerCAmelCase   (       ):
			return sum(
			    {
			        int("".join(pandigital[5:9]		)		)
			        for pandigital in itertools.permutations("123456789"		)
			        if is_combination_valid(snake_case__		)
			    }		)


if __name__ == "__main__":
				print(solution())



