code: def solve():
      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)
      lastn = 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 factors(n):
          """Returns a prime factors of n as a list"""
          _refresh(n)
          x, xp, f = 0, prime_list[0], []
          while xp <= n:
              if not n % xp:
                  f.append(xp)
                  n = n / xp
              else:
                  x = x + 1
                  xp = prime_list[x]
          return f
  
      def all_factors(n):
          """Returns all factors of n, including 1 and n"""
          f = factors(n)
          elts = sorted(set(f))
          numelts = len(elts)
  
          def gen_inner(i):
              if i >= numelts:
                  yield 1
                  return
              thiselt = elts[i]
              thismax = f.count(thiselt)
              powers = [1]
              for j in range(thismax):
                  powers.append(powers[-1] * thiselt)
              for d in gen_inner(i + 1):
                  for prime_power in powers:
                      yield prime_power * d
  
          for d in gen_inner(0):
              yield d
  
      MAX = 28124
      _refresh(MAX / 2)
      abundants = [
          n for n in range(1, MAX) if sum(all_factors(n)) > n + n
      ]
      abundants_dict = dict.fromkeys(abundants, 1)
  
      total = 0
      for n in range(1, MAX):
          sum_of_abundants = 0
          for a in abundants:
              if a > n:
                  break
              if abundants_dict.get(n - a):
                  sum_of_abundants = 1
                  break
              if not sum_of_abundants:
                  total = total + n
  
      return total
  
label_desc: Use image node_id 1 for calling a global function with example usage: solve() and returns: total, isprime, f