# Definition (Primorial Of a Number)

*Is similar to factorial of a number*, **_In primorial_**, not all the natural numbers get multiplied, **_only prime numbers are multiplied to calculate the primorial of a number_**. It's denoted with **_P_****_#_** and it is the product of the first n prime numbers.
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# Task

**_Given_** *a number N* , **_calculate its primorial_**. ![!alt](https://i.imgur.com/mdX8dJP.png)  ![!alt](https://i.imgur.com/mdX8dJP.png)  
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# Notes

* **_Only positive_** numbers *will be passed (N > 0)* .
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# Input >> Output Examples:

``` cpp
1- numPrimorial (3) ==> return (30)
```

## **_Explanation_**:

**_Since_** *the passed number is (3)* ,**_Then_** **_the primorial_** *should obtained by multiplying*  ```2 * 3 * 5 = 30 .```

### Mathematically written as , **_P_**3**_#_** = 30 .
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## **_Explanation_**:

**_Since_** *the passed number is (5)* ,**_Then_** **_the primorial_** *should obtained by multiplying*  ``` 2 * 3 * 5 * 7 * 11 = 2310 .```

### Mathematically written as , **_P_**5**_#_** = 2310 .
___

## **_Explanation_**: 

**_Since_** *the passed number is (6)* ,**_Then_** **_the primorial_** *should obtained by multiplying*  ``` 2 * 3 * 5 * 7 * 11 * 13 = 30030 .```

### Mathematically written as , **_P_**6**_#_** = 30030 .
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# [Playing with Numbers Series](https://www.codewars.com/collections/playing-with-numbers)

# [Playing With Lists/Arrays Series](https://www.codewars.com/collections/playing-with-lists-slash-arrays)

# [For More Enjoyable Katas](http://www.codewars.com/users/MrZizoScream/authored)
___

## ALL translations are welcomed

## Enjoy Learning !!
# Zizou

```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 = 'def num_primorial(n):\n    """\n    Custom Sieve method used...\n    """\n    prime_list = [2]\n    ans = prime_list[0]\n    chk_num = 3\n    while len(prime_list) != n:\n        for prime in prime_list:\n            if chk_num % prime == 0:\n               break\n            elif prime == prime_list[-1]: # and chk_num%prime != 0\n                prime_list.append(chk_num)   # chk_num is prime\n                ans = ans*prime_list[-1] # update answer\n        chk_num = chk_num + 2 #all primes after 2 are odd\n    return ans\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'num_primorial'
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: 5498