






'''simple docstring'''





from __future__ import annotations

import math






def    lowerCamelCase_     (    lowercase__):

 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


__A							:							str  							=		[num for num in range(3, 10_00_01, 2) if not is_prime(num)]






def    lowerCamelCase_     (    lowercase__):
 if not isinstance(lowercase__				,     lowercase__):
  raise ValueError("n must be an integer")
 if n <= 0:
  raise ValueError("n must be >= 0")

 lowerCamelCase__  =     []
 for num in range(len(lowercase__)):
  lowerCamelCase__  =     0
  while 2 * i * i <= odd_composites[num]:
   lowerCamelCase__  =     odd_composites[num] - 2 * i * i
   if is_prime(lowercase__):
    break
   i += 1
  else:
   list_nums.append(odd_composites[num])
   if len(lowercase__) == n:
    return list_nums

 return []






def    lowerCamelCase_     (    ):
 return compute_nums(1)[0]


if __name__ == "__main__":
 print(F"""{solution() = }""")









'''simple docstring'''





from decimal import Decimal, getcontext
from math import ceil, factorial






def    lowerCamelCase_     (    lowercase__):

 if not isinstance(lowercase__				,     lowercase__):
  raise TypeError("Undefined for non-integers")
 elif precision < 1:
  raise ValueError("Undefined for non-natural numbers")

 lowerCamelCase__  =     precision
 lowerCamelCase__  =     ceil(precision / 14)
 lowerCamelCase__  =     426880 * Decimal(10005).sqrt()
 lowerCamelCase__  =     1
 lowerCamelCase__  =     13591409
 lowerCamelCase__  =     Decimal(lowercase__)
 for k in range(1				,     lowercase__):
  lowerCamelCase__  =     factorial(6 * k) // (factorial(3 * k) * factorial(lowercase__) ** 3)
  linear_term += 545140134
  exponential_term *= -262537412640768000
  partial_sum += Decimal(multinomial_term * linear_term) / exponential_term
 return str(constant_term / partial_sum)[:-1]


if __name__ == "__main__":
 __A							:							Dict  							=		50
 print(F"""The first {n} digits of pi is: {pi(n)}""")

