


'''simple docstring'''







import math







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







def _UpperCamelCase			(	__A = 1000 ,     __A = 1000       )				->						int:


      '''simple docstring'''



      UpperCamelCase__      =							[0, 0, 0]  # length, a, b
      for a in range((a_limit * -1) + 1 ,     __A       ):
            for b in range(2 ,     __A       ):
                  if is_prime(__A       ):
                        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(1_0_0_0, 1_0_0_0))









'''simple docstring'''







import itertools







def _UpperCamelCase			(	__A = 1000000       )				->						int:


      '''simple docstring'''



      UpperCamelCase__      =							[1]

      for i in itertools.count(len(__A       )       ):
            UpperCamelCase__      =							0
            for j in itertools.count(1       ):
                  UpperCamelCase__      =							-1 if j % 2 == 0 else +1
                  UpperCamelCase__      =							(j * j * 3 - j) // 2
                  if index > i:
                        break
                  item += partitions[i - index] * sign
                  item %= number
                  index += j
                  if index > i:
                        break
                  item += partitions[i - index] * sign
                  item %= number

            if item == 0:
                  return i
            partitions.append(__A       )

      return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(F"""{solution() = }""")





