Generate and return **all** possible increasing arithmetic progressions of six primes `[a, b, c, d, e, f]` between the given limits. Note: the upper and lower limits are inclusive.

An arithmetic progression is a sequence where the difference between consecutive numbers is the same, such as: 2, 4, 6, 8.

A prime number is a number that is divisible only by itself and 1 (e.g. 2, 3, 5, 7, 11)

Your solutions should be returned as lists inside a list in ascending order of the first item (if there are multiple lists with same first item, return in ascending order for the second item etc) are the e.g: `[ [a, b, c, d, e, f], [g, h, i, j, k, l] ]` where `a < g`. If there are no solutions, return an empty list: `[]`

## Examples

```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 = 'LIMIT = 10**4\nsieve = list(range(LIMIT))\nsieve[1] = 0\nprimes = []\nfor n in sieve:\n    if n:\n        primes.append(n)\n        for i in range(n*n, LIMIT, n):\n            sieve[i] = 0\n\ndel sieve\nprimes.remove(2)\n\n\ndef primes_a_p(lower_limit, upper_limit, k=6):\n    primes_list = [ p for p in primes if lower_limit <= p <= upper_limit ]\n    primes_set = set(primes_list)\n    \n    max_scope = (upper_limit - lower_limit) // (k-1)\n    \n    #base_diff = reduce(mul, [ p for p in primes if p <= k ])\n    base_diff = 2 * 3 * 5\n    \n    solutions = []\n    \n    for n in range(1, max_scope // base_diff + 1):\n        diffs = [ n * base_diff * x for x in range(k) ]\n        scope = n * base_diff * (k-1)\n        \n        for p in primes_list:\n            if p + scope > upper_limit:\n                break\n            \n            if { p+d for d in diffs } <= primes_set:\n                solutions.append([ p + d for d in diffs ])\n    \n    return sorted(solutions)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'primes_a_p'
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: 9848