import itertools
import math




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




def    lowerCAmelCase_  (		)     ->					Any:







 '''simple docstring'''
 _UpperCamelCase:  Optional[Any]    						=			2
 while True:
  if is_prime(lowercase		):
   yield num
  num += 1




def    lowerCAmelCase_  (		lowercase:				int = 10_001		)     ->					int:







 '''simple docstring'''
 return next(itertools.islice(prime_generator()	,       nth - 1	,       lowercase		)		)


if __name__ == "__main__":
  print(f"""{solution() = }""")
import random




def    lowerCAmelCase_  (		lowercase:				int	,       lowercase:				float	,       lowercase:				bool = False		)     ->					dict:







 '''simple docstring'''
 _UpperCamelCase:  dict    						=			{i: [] for i in range(lowercase		)}

 # if probability is greater or equal than 1, then generate a complete graph
 if probability >= 1:
  return complete_graph(lowercase		)
 # if probability is lower or equal than 0, then return a graph without edges
 if probability <= 0:
  return graph

 # for each couple of nodes, add an edge from u to v
 # if the number randomly generated is greater than probability probability
 for i in range(lowercase		):
  for j in range(i + 1	,       lowercase		):
   if random.random() < probability:
    graph[i].append(lowercase		)
    if not directed:
     # if the graph is undirected, add an edge in from j to i, either
     graph[j].append(lowercase		)
 return graph




def    lowerCAmelCase_  (		lowercase:				int		)     ->					dict:







 '''simple docstring'''
 return {
     i: [j for j in range(lowercase		) if i != j] for i in range(lowercase		)
 }


if __name__ == "__main__":
  import doctest

  doctest.testmod()