Consider the range `0` to `10`. The primes in this range are: `2, 3, 5, 7`, and thus the prime pairs are: `(2,2), (2,3), (2,5), (2,7), (3,3), (3,5), (3,7),(5,5), (5,7), (7,7)`.

Let's take one pair `(2,7)` as an example and get the product, then sum the digits of the result as follows:  `2 * 7 = 14`, and `1 + 4 = 5`. We see that `5` is a prime number. Similarly, for the pair `(7,7)`, we get: `7 * 7 = 49`, and `4 + 9 = 13`, which is a prime number. 

You will be given a range and your task is to return the number of pairs that revert to prime as shown above. In the range `(0,10)`, there are only `4` prime pairs that end up being primes in a similar way: `(2,7), (3,7), (5,5), (7,7)`. Therefore, `solve(0,10) = 4)`

Note that the upperbound of the range will not exceed `10000`. A range of `(0,10)` means that: `0 <= n < 10`.

Good luck!

If you like this Kata, please try 

[Simple Prime Streaming](https://www.codewars.com/kata/5a908da30025e995880000e3)

[Prime reduction](https://www.codewars.com/kata/59aa6567485a4d03ff0000ca)

[Dominant primes](https://www.codewars.com/kata/59ce11ea9f0cbc8a390000ed)

```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 = 'from itertools import compress, combinations_with_replacement\nimport numpy as np\n\n\ns = np.ones(10001)\ns[:2] = s[4::2] = 0\nfor i in range(3, int(len(s)**0.5)+1, 2):\n    if s[i]:\n        s[i*i::i] = 0\nPRIMES = list(compress(list(range(len(s))), s))\n\ndef solve(a, b):\n    i, j = np.searchsorted(PRIMES, a), np.searchsorted(PRIMES, b)\n    return sum(s[sum(map(int, str(x * y)))] for x, y in combinations_with_replacement(PRIMES[i:j], 2))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'solve'
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: 17710