






import math


def __A					(   __lowerCAmelCase			)->						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(__lowerCAmelCase			) + 1			)				,	6			):
												if number % i == 0 or number % (i + 2) == 0:
																		return False
						return True


def __A					(   __lowerCAmelCase = 1_000				,	__lowerCAmelCase = 1_000			)->						int:





						"""simple docstring"""



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


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








from itertools import combinations_with_replacement


def __A					(   __lowerCAmelCase = 100			)->						int:





						"""simple docstring"""



						_UpperCAmelCase             =    [*list(range(1				,	21			)			), 25]
						_UpperCAmelCase             =    [2 * x for x in range(1				,	21			)] + [50]
						_UpperCAmelCase             =    [3 * x for x in range(1				,	21			)]
						_UpperCAmelCase             =    singles + doubles + triples + [0]

						_UpperCAmelCase             =    0
						_UpperCAmelCase             =    42
						_UpperCAmelCase             =    42
						_UpperCAmelCase             =    42
						_UpperCAmelCase             =    42

						for double in doubles:
												for throwa, throwa in combinations_with_replacement(__lowerCAmelCase				,	2			):
																		_UpperCAmelCase             =    double + throwa + throwa
																		if checkout_total < limit:
																								num_checkouts += 1

						return num_checkouts


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