

'''simple docstring'''







import math






def 					_SCREAMING_SNAKE_CASE		(						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 					_SCREAMING_SNAKE_CASE		(						snake_case_ = 1000							,       snake_case_ = 1000	):
	_lowercase							=     [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_	):
				_lowercase							=     0
				_lowercase							=     0
				while is_prime((n**2) + (a * n) + b	):
					count += 1
					n += 1
				if count > longest[0]:
					_lowercase							=     [count, a, b]
	_lowercase							=     longest[1] * longest[2]
	return ans


if __name__ == "__main__":
							print(solution(1_0_0_0, 1_0_0_0))







'''simple docstring'''







from __future__ import annotations

import math
import random






def 					_SCREAMING_SNAKE_CASE		(						snake_case_							,       snake_case_							,       snake_case_	):
	_lowercase							=     d * e - 1
	_lowercase							=     0
	_lowercase							=     0
	while p == 0:
		_lowercase							=     random.randint(2							,       n - 1	)
		_lowercase							=     k
		while True:
			if t % 2 == 0:
				_lowercase							=     t // 2
				_lowercase							=     (g**t) % n
				_lowercase							=     math.gcd(x - 1							,       snake_case_	)
				if x > 1 and y > 1:
					_lowercase							=     y
					_lowercase							=     n // y
					break  # find the correct factors
			else:
				break  # t is not divisible by 2, break and choose another g
	return sorted([p, q]	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




