*This is the advanced version of the [Total Primes](https://www.codewars.com/kata/total-primes/) kata.*

---

The number `23` is the smallest prime that can be "cut" into **multiple** primes: `2, 3`. Another such prime is `6173`, which can be cut into `61, 73` or `617, 3` or `61, 7, 3` (all primes). A third one is `557` which can be sliced into `5, 5, 7`. Let's call these numbers **total primes**.

Notes:
* one-digit primes are excluded by definition;
* leading zeros are also excluded: e.g. splitting `307` into `3, 07` is **not** valid


## Task

Complete the function that takes a range `[a..b]` (both limits included) and returns the total primes within that range (`a ≤ total primes ≤ b`).

The tests go up to 10^(6).
~~~if:python
For your convenience, a list of primes up to 10^(6) is preloaded, called `PRIMES`.
~~~


## Examples
```
(0, 100)  ==>  [23, 37, 53, 73]

(500, 600) ==> [523, 541, 547, 557, 571, 577, 593]
```
Happy coding!

---

## My other katas

If you enjoyed this kata then please try [my other katas](https://www.codewars.com/collections/katas-created-by-anter69)! :-)

#### *Translations are welcome!*

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import numpy as np\nfrom itertools import accumulate\ndef sieve_primes(n):\n    sieve = np.ones(n // 2, dtype = np.bool)\n    limit = 1 + int(n ** 0.5)\n\n    for a in range(3, limit, 2):\n        if sieve[a // 2]:\n            sieve[a * a // 2::a] = False\n\n    prime_indexes = 2 * np.nonzero(sieve)[0].astype(int) + 1\n    prime_indexes[0] = 2\n    return set(map(str, prime_indexes))\n\nprimes = sieve_primes(10 ** 6)\n\ndef all_primes(s):\n    if int(s) < 10:\n        return s in primes\n    for n in accumulate(s[:-1]):\n        if n in primes:\n            m = s[len(n):]\n            if m in primes or all_primes(m):\n                return True\n\ndef total_primes(a, b):\n    return [int(a) for a in map(str, range(max(10, a), b + 1)) if a in primes and all_primes(a)]'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'total_primes'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6285