

import math
def 						UpperCamelCase_(			snake_case__:  int   )       -> bool:

 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 						UpperCamelCase_(			snake_case__:  int = 10_00  ,    snake_case__:  int = 10_00   )       -> int:
 UpperCAmelCase__							=				[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__							=				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))






def 						UpperCamelCase_(			snake_case__:  list   )       -> list:
 UpperCAmelCase__							=				len(snake_case__   )

 # Set the gap value to be decreased by a factor of 1.3
 # after each iteration
 UpperCAmelCase__							=				1.3

 # Continue sorting until the gap is 1
 while gap > 1:
  # Decrease the gap value
  UpperCAmelCase__							=				int(gap / shrink   )

  # Sort the elements using insertion sort
  for i in range(snake_case__  ,    len(snake_case__   )   ):
   UpperCAmelCase__							=				collection[i]
   UpperCAmelCase__							=				i
   while j >= gap and collection[j - gap] > temp:
    UpperCAmelCase__							=				collection[j - gap]
    j -= gap
   UpperCAmelCase__							=				temp

 return collection


if __name__ == "__main__":
 import doctest

 doctest.testmod()



