code: 
  
  
  
  
  
  '''simple docstring'''
  
  
  
  
  
  
  
  import math
  
  
  
  
  
  def      _lowerCAmelCase		(		lowercase			)      ->      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(lowercase			) + 1			)      ,			6			):
  						if number % i == 0 or number % (i + 2) == 0:
  									return False
  			return True
  
  
  
  
  
  def      _lowerCAmelCase		(		lowercase = 1000      ,			lowercase = 1000			)      ->      int:
  			__lowerCAmelCase      		=       [0, 0, 0]  # length, a, b
  			for a in range((a_limit * -1) + 1      ,			lowercase			):
  						for b in range(2      ,			lowercase			):
  									if is_prime(lowercase			):
  												__lowerCAmelCase      		=       0
  												__lowerCAmelCase      		=       0
  												while is_prime((n**2) + (a * n) + b			):
  															count += 1
  															n += 1
  												if count > longest[0]:
  															__lowerCAmelCase      		=       [count, a, b]
  			__lowerCAmelCase      		=       longest[1] * longest[2]
  			return ans
  
  
  if __name__ == "__main__":
  	print(solution(1_0_0_0, 1_0_0_0))
  
  
style_context: 
  
  
  
  
  
  '''simple docstring'''
  
  
  
  
  
  
  
  from __future__ import annotations
  
  from collections.abc import Iterable, Iterator
  from typing import Any, Generic, TypeVar
  
  _a      :				Dict											=					TypeVar("""T""", bound=bool)
  
  
  
  
  
  class 					_UpperCAmelCase							(		Generic[T]     ):
  		def __init__(						self,__SCREAMING_SNAKE_CASE    ):
  
  
  
  					'''simple docstring'''
  
  					__lowerCAmelCase      		=       value
  					__lowerCAmelCase      		=       None
  					__lowerCAmelCase      		=       None
  		@property
  		def 						lowerCamelCase__    (						self    ):
  
  
  
  					'''simple docstring'''
  
  					return self._value
  
  
  
  
  
  
  
  		@staticmethod
  		def 						lowerCamelCase__    (						__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE    ):
  
  
  
  					'''simple docstring'''
  
  					if not roota:
  								return roota
  
  					if not roota:
  								return roota
  
  					if roota.value > roota.value:
  								__lowerCAmelCase		, __lowerCAmelCase      		=       roota, roota
  
  					__lowerCAmelCase      		=       roota
  					__lowerCAmelCase      		=       roota.right
  					__lowerCAmelCase      		=       roota.left
  					__lowerCAmelCase      		=       SkewNode.merge(__SCREAMING_SNAKE_CASE,__SCREAMING_SNAKE_CASE    )
  
  					return result
  
  
  
  
  
  class 					_UpperCAmelCase							(		Generic[T]     ):
  		def __init__(						self,__SCREAMING_SNAKE_CASE = ()    ):
  
  
  
  					'''simple docstring'''
  
  					__lowerCAmelCase      		=       None
  					if data:
  								for item in data:
  											self.insert(__SCREAMING_SNAKE_CASE    )
  		def __bool__(						self    ):
  
  
  
  					'''simple docstring'''
  
  					return self._root is not None
  		def __iter__(						self    ):
  
  
  
  					'''simple docstring'''
  
  					__lowerCAmelCase      		=       []
  					while self:
  								result.append(self.pop()    )
  
  					# Pushing items back to the heap not to clear it.
  					for item in result:
  								self.insert(__SCREAMING_SNAKE_CASE    )
  
  					return iter(__SCREAMING_SNAKE_CASE    )
  		def 						lowerCamelCase__    (						self,__SCREAMING_SNAKE_CASE    ):
  
  
  
  					'''simple docstring'''
  
  					__lowerCAmelCase      		=       SkewNode.merge(self._root,SkewNode(__SCREAMING_SNAKE_CASE    )    )
  		def 						lowerCamelCase__    (						self    ):
  
  
  
  					'''simple docstring'''
  
  					__lowerCAmelCase      		=       self.top()
  					__lowerCAmelCase      		=       (
  					    SkewNode.merge(self._root.left,self._root.right    ) if self._root else None
  					)
  
  					return result
  		def 						lowerCamelCase__    (						self    ):
  
  
  
  					'''simple docstring'''
  
  					if not self._root:
  								raise IndexError("""Can't get top element for the empty heap."""    )
  					return self._root.value
  
  
  
  
  
  
  
  		def 						lowerCamelCase__    (						self    ):
  
  
  
  					'''simple docstring'''
  
  					__lowerCAmelCase      		=       None
  
  
  if __name__ == "__main__":
  	import doctest
  
  	doctest.testmod()
  
  