



"""simple docstring"""
def    _snake_case		(		UpperCamelCase		:	int		):
 assert isinstance(UpperCamelCase    ,	UpperCamelCase		), F"The input value of [n={number}] is not an integer"

 if number == 1:
  return 2
 elif number < 1:
  UpperCAmelCase			:      str			=			F"The input value of [n={number}] has to be > 0"
  raise ValueError(UpperCamelCase		)
 else:
  UpperCAmelCase			:      Dict			=			sylvester(number - 1		)
  UpperCAmelCase			:      Tuple			=			num - 1
  UpperCAmelCase			:      List[str]			=			num
  return lower * upper + 1


if __name__ == "__main__":
      print(f"""The 8th number in Sylvester's sequence: {sylvester(8)}""")





"""simple docstring"""
from __future__ import annotations

from collections.abc import Generator

def    _snake_case		(		):
 UpperCAmelCase			:      dict[int, int]			=			{}
 UpperCAmelCase			:      str			=			2
 while True:
  UpperCAmelCase			:      List[str]			=			factor_map.pop(UpperCamelCase    ,	UpperCamelCase		)
  if factor:
   UpperCAmelCase			:      Dict			=			factor + prime
   while x in factor_map:
    x += factor
   UpperCAmelCase			:      Tuple			=			factor
  else:
   UpperCAmelCase			:      Optional[int]			=			prime
   yield prime
  prime += 1

def    _snake_case		(		UpperCamelCase		:	float = 1e1_0		):
 UpperCAmelCase			:      Tuple			=			sieve()

 UpperCAmelCase			:      Optional[Any]			=			1
 while True:
  UpperCAmelCase			:      List[str]			=			next(UpperCamelCase		)
  if (2 * prime * n) > limit:
   return n
  # Ignore the next prime as the reminder will be 2.
  next(UpperCamelCase		)
  n += 2


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