code: def solve():
      """
      It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
  
       9 =  7 + 2 x 1^2
      15 =  7 + 2 x 2^2
      21 =  3 + 2 x 3^2
      25 =  7 + 2 x 3^2
      27 = 19 + 2 x 2^2
      33 = 31 + 2 x 1^2
      It turns out that the conjecture was false.
  
      What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
      """
  
      prime_list = [
          2,
          3,
          5,
          7,
          11,
          13,
          17,
          19,
          23,
      ]  # Ensure that this is initialised with at least 1 prime
      prime_dict = dict.fromkeys(prime_list, 1)
  
      def _isprime(n):
          """Raw check to see if n is prime. Assumes that prime_list is already populated"""
          isprime = n >= 2 and 1 or 0
          for prime in prime_list:  # Check for factors with all primes
              if prime * prime > n:
                  break  # ... up to sqrt(n)
              if not n % prime:
                  isprime = 0
                  break
          if isprime:
              prime_dict[n] = 1  # Maintain a dictionary for fast lookup
          return isprime
  
      def _refresh(x):
          """Refreshes primes upto x"""
          lastn = prime_list[-1]
          while lastn <= x:  # Keep working until we've got up to x
              lastn = lastn + 1  # Check the next number
              if _isprime(lastn):
                  prime_list.append(
                      lastn
                  )  # Maintain a list for sequential access
  
      def prime(x):
          """Returns the xth prime"""
  
          lastn = prime_list[-1]
          while (
              len(prime_list) <= x
          ):  # Keep working until we've got the xth prime
              lastn = lastn + 1  # Check the next number
              if _isprime(lastn):
                  prime_list.append(
                      lastn
                  )  # Maintain a list for sequential access
          return prime_list[x]
  
      MAX = 10000
      squares = dict.fromkeys((x * x for x in range(1, MAX)), 1)
      _refresh(MAX)
  
      for x in range(35, MAX, 2):
          if not _isprime(x):
              is_goldbach = 0
              for p in prime_list[1:]:
                  if p >= x:
                      break
                  if ((x - p) / 2) in squares:
                      is_goldbach = 1
                      break
              if not is_goldbach:
                  return x
                  break
  
label_desc: Use image node_id 1 for calling a global function with example usage: solve() and returns: isprime, prime_list, x